{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.dates as mdates\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from sympy import Symbol, symbols, Matrix, sin, cos\n",
    "from sympy import init_printing\n",
    "from sympy.utilities.codegen import codegen\n",
    "init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter Implementation for Constant Turn Rate and Acceleration (CTRA) Vehicle Model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Wikipedia](http://en.wikipedia.org/wiki/Extended_Kalman_filter) writes: In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.\n",
    "\n",
    "$\\boldsymbol{x}_{k} = g(\\boldsymbol{x}_{k-1}, \\boldsymbol{u}_{k-1}) + \\boldsymbol{w}_{k-1}$\n",
    "\n",
    "$\\boldsymbol{z}_{k} = h(\\boldsymbol{x}_{k}) + \\boldsymbol{v}_{k}$\n",
    "\n",
    "Where $w_k$ and $v_k$ are the process and observation noises which are both assumed to be zero mean Multivariate Gaussian noises with covariance matrix $Q$ and $R$ respectively.\n",
    "\n",
    "The function $g$ can be used to compute the predicted state from the previous estimate and similarly the function $h$ can be used to compute the predicted measurement from the predicted state. However, $g$ and $h$ cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian matrix) is computed.\n",
    "\n",
    "At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Situation covered: You have a velocity sensor, which measures the vehicle speed ($v$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector - Constant Turn Rate and Acceleration Vehicle Model (CTRA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constant Turn Rate, Constant Velocity Model for a vehicle ![CTRV Model](CTRV-Model.png)\n",
    "\n",
    "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\\\ a} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\\\ \\text{longitudinal acceleration}} \\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "numstates=6 # States"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n",
    "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "vs, psis, dpsis, dts, xs, ys, lats, lons, axs = symbols('v \\psi \\dot\\psi T x y lat lon a')\n",
    "\n",
    "gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))],\n",
    "             [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))],\n",
    "             [psis+dpsis*dts],\n",
    "             [axs*dts + vs],\n",
    "             [dpsis],\n",
    "             [axs]])\n",
    "state = Matrix([xs,ys,psis,vs,dpsis,axs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This formulas calculate how the state is evolving from one to the next time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x + \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y + \\frac{v}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\T a + v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡    v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "⎢x + ───────────────────────────────────────⎥\n",
       "⎢                    \\dot\\psi               ⎥\n",
       "⎢                                           ⎥\n",
       "⎢    v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "⎢y + ────────────────────────────────────── ⎥\n",
       "⎢                   \\dot\\psi                ⎥\n",
       "⎢                                           ⎥\n",
       "⎢             T⋅\\dot\\psi + \\psi             ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                  T⋅a + v                  ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                 \\dot\\psi                  ⎥\n",
       "⎢                                           ⎥\n",
       "⎣                     a                     ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the Jacobian of the Dynamic Matrix with respect to the state vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢  \\psi  ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎢\\dot\\psi⎥\n",
       "⎢        ⎥\n",
       "⎣   a    ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & \\frac{v}{\\dot\\psi} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & 0\\\\0 & 1 & \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & 0\\\\0 & 0 & 1 & 0 & T & 0\\\\0 & 0 & 0 & 1 & 0 & T\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      v⋅(-cos(\\psi) + cos(T⋅\\dot\\psi + \\psi))  -sin(\\psi) + sin(T⋅\\dot\\psi + \n",
       "⎢1  0  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                               \\dot\\psi        \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢      v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))  cos(\\psi) - cos(T⋅\\dot\\psi + \\\n",
       "⎢0  1  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                              \\dot\\psi         \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0  0                     1                                      0            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      1            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      0            \n",
       "⎢                                                                             \n",
       "⎣0  0                     0                                      0            \n",
       "\n",
       "\\psi)  T⋅v⋅cos(T⋅\\dot\\psi + \\psi)   v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))   \n",
       "─────  ────────────────────────── - ───────────────────────────────────────  0\n",
       "                \\dot\\psi                                   2                  \n",
       "                                                   \\dot\\psi                   \n",
       "                                                                              \n",
       "psi)   T⋅v⋅sin(T⋅\\dot\\psi + \\psi)   v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi))    \n",
       "────   ────────────────────────── - ──────────────────────────────────────   0\n",
       "                \\dot\\psi                                  2                   \n",
       "                                                  \\dot\\psi                    \n",
       "                                                                              \n",
       "                                        T                                    0\n",
       "                                                                              \n",
       "                                        0                                    T\n",
       "                                                                              \n",
       "                                        1                                    0\n",
       "                                                                              \n",
       "                                        0                                    1\n",
       "\n",
       "⎤\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎥\n",
       "⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has to be computed on every filter step because it consists of state variables!\n",
    "\n",
    "To Sympy Team: A `.to_python` and `.to_c` and `.to_matlab` whould be nice to generate code, like it already works with `print latex()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial Uncertainty $P_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialized with $0$ means you are pretty sure where the vehicle starts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1000.,     0.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,  1000.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,  1000.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,  1000.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,  1000.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,     0.,  1000.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Noise Covariance Matrix Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"*The state uncertainty model models the disturbances which excite the linear system. Conceptually, it estimates how bad things can get when the system is run open loop for a given period of time.*\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  3.09760000e-06,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   3.09760000e-06,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   4.00000000e-06,\n",
      "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          3.09760000e-02,   0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   4.00000000e-04,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00,   2.50000000e-01]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "sGPS     = 0.5*8.8*dt**2  # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sCourse  = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle\n",
    "sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sYaw     = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle\n",
    "sAccel   = 0.5\n",
    "\n",
    "Q = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2, sAccel**2])\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/paul/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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YEdNq7ZubPg/4lqRTgGXAcXXPI6LhoYp+kxQDeTwzaz+SiIiaGVRSTJs2rak2FyxYULfN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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107df0ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(9))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(8),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(9))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(8),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read '2014-03-26-000-Data.csv' successfully.\n"
     ]
    }
   ],
   "source": [
    "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n",
    "datafile = '2014-03-26-000-Data.csv'\n",
    "\n",
    "date, \\\n",
    "time, \\\n",
    "millis, \\\n",
    "ax, \\\n",
    "ay, \\\n",
    "az, \\\n",
    "rollrate, \\\n",
    "pitchrate, \\\n",
    "yawrate, \\\n",
    "roll, \\\n",
    "pitch, \\\n",
    "yaw, \\\n",
    "speed, \\\n",
    "course, \\\n",
    "latitude, \\\n",
    "longitude, \\\n",
    "altitude, \\\n",
    "pdop, \\\n",
    "hdop, \\\n",
    "vdop, \\\n",
    "epe, \\\n",
    "fix, \\\n",
    "satellites_view, \\\n",
    "satellites_used, \\\n",
    "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n",
    "                  converters={1: mdates.strpdate2num('%H%M%S%f'),\n",
    "                              0: mdates.strpdate2num('%y%m%d')},\n",
    "                  skiprows=1)\n",
    "\n",
    "print('Read \\'%s\\' successfully.' % datafile)\n",
    "\n",
    "# A course of 0° means the Car is traveling north bound\n",
    "# and 90° means it is traveling east bound.\n",
    "# In the Calculation following, East is Zero and North is 90°\n",
    "# We need an offset.\n",
    "course =(-course+90.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Function H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix $J_H$ is the Jacobian of the Measurement function $h$ with respect to the state. Function $h$ can be used to compute the predicted measurement from the predicted state.\n",
    "\n",
    "If a GPS measurement is available, the following function maps the state to the measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\v\\\\\\dot\\psi\\\\a\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎢\\dot\\psi⎥\n",
       "⎢        ⎥\n",
       "⎣   a    ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hs = Matrix([[xs],\n",
    "             [ys],\n",
    "             [vs],\n",
    "             [dpsis],\n",
    "             [axs]])\n",
    "hs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0  0  0  0  0⎤\n",
       "⎢                ⎥\n",
       "⎢0  1  0  0  0  0⎥\n",
       "⎢                ⎥\n",
       "⎢0  0  0  1  0  0⎥\n",
       "⎢                ⎥\n",
       "⎢0  0  0  0  1  0⎥\n",
       "⎢                ⎥\n",
       "⎣0  0  0  0  0  1⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JHs=hs.jacobian(state)\n",
    "JHs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If no GPS measurement is available, simply set the corresponding values in $J_h$ to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurement Noise Covariance $R$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  2.50000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   2.50000000e+01,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   9.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          1.00000000e-02,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   1.00000000e+00]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "varGPS = 5.0 # Standard Deviation of GPS Measurement\n",
    "varspeed = 3.0 # Variance of the speed measurement\n",
    "varyaw = 0.1 # Variance of the yawrate measurement\n",
    "varacc = 1.0 # Variance of the longitudinal Acceleration\n",
    "R = np.diag([varGPS**2, varGPS**2, varspeed**2, varyaw**2, varacc**2])\n",
    "\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8C1gDGAfMiIiXK5afCqwXETM7FqWZ9YQyt9hOAr4CPA0sIQ3AcCmseELmEcBlnQrQzHpH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\nVjpObGZWOk5sZlY6/x9IvKujVg3rwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107df04d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4.5, 4.5))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$v$', '$\\dot \\psi$', '$a$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  1.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(numstates)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approx. Lat/Lon to Meters to check Location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RadiusEarth = 6378388.0 # m\n",
    "arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/°\n",
    "\n",
    "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n",
    "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n",
    "\n",
    "mx = np.cumsum(dx)\n",
    "my = np.cumsum(dy)\n",
    "\n",
    "ds = np.sqrt(dx**2+dy**2)\n",
    "\n",
    "GPS=np.hstack((True, (np.diff(ds)>0.0).astype('bool'))) # GPS Trigger for Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.        ],\n",
      "        [ 0.        ],\n",
      "        [-4.08756111],\n",
      "        [ 0.67322222],\n",
      "        [-0.32660346],\n",
      "        [ 0.2647    ]]), (6, 1))\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUoAAAAWCAYAAACmEtU9AAAABHNCSVQICAgIfAhkiAAABThJREFU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\n8kRIpVaRSCQSiUQikUgkEolMBf4DWgW1csY3di4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( -0.002, \\quad 0.002, \\quad -0.003, \\quad 0.003\\right )$$"
      ],
      "text/plain": [
       "(-0.002, 0.002, -0.003, 0.003)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108eb15d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi, ax[0]]]).T\n",
    "print(x, x.shape)\n",
    "\n",
    "U=float(np.cos(x[2])*x[3])\n",
    "V=float(np.sin(x[2])*x[3])\n",
    "\n",
    "plt.quiver(x[0], x[1], U, V)\n",
    "plt.scatter(float(x[0]), float(x[1]), s=100)\n",
    "plt.title('Initial Location')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put everything together as a measurement vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5, 10800)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi, ax))\n",
    "# Lenth of the measurement\n",
    "m = measurements.shape[1]\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "x0 = []\n",
    "x1 = []\n",
    "x2 = []\n",
    "x3 = []\n",
    "x4 = []\n",
    "x5 = []\n",
    "x6 = []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Pdv =[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "Kdv= []\n",
    "dstate=[]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\\\ a \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\\\ \\text{acceleration} \\end{bmatrix} =  \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4] \\\\ x[5]  \\end{matrix}}_{\\textrm{Python Nomenclature}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "\n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    # see \"Dynamic Matrix\"\n",
    "    if np.abs(yawrate[filterstep])<0.0001: # Driving straight\n",
    "        x[0] = x[0] + x[3]*dt * np.cos(x[2])\n",
    "        x[1] = x[1] + x[3]*dt * np.sin(x[2])\n",
    "        x[2] = x[2]\n",
    "        x[3] = x[3] + x[5]*dt\n",
    "        x[4] = 0.0000001 # avoid numerical issues in Jacobians\n",
    "        x[5] = x[5]\n",
    "        dstate.append(0)\n",
    "    else: # otherwise\n",
    "        x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2]))\n",
    "        x[1] = x[1] + (x[3]/x[4]) * (-np.cos(x[4]*dt+x[2])+ np.cos(x[2]))\n",
    "        x[2] = (x[2] + x[4]*dt + np.pi) % (2.0*np.pi) - np.pi\n",
    "        x[3] = x[3] + x[5]*dt\n",
    "        x[4] = x[4] # Constant Turn Rate\n",
    "        x[5] = x[5] # Constant Acceleration\n",
    "        dstate.append(1)\n",
    "    \n",
    "    # Calculate the Jacobian of the Dynamic Matrix A\n",
    "    # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n",
    "    a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n",
    "    a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    JA = np.matrix([[1.0, 0.0, a13, a14, a15, 0.0],\n",
    "                    [0.0, 1.0, a23, a24, a25, 0.0],\n",
    "                    [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    \n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = JA*P*JA.T + Q\n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Measurement Function\n",
    "    hx = np.matrix([[float(x[0])],\n",
    "                    [float(x[1])],\n",
    "                    [float(x[3])],\n",
    "                    [float(x[4])],\n",
    "                    [float(x[5])]])\n",
    "\n",
    "    if GPS[filterstep]: # with 10Hz, every 5th step\n",
    "        JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    else: # every other step\n",
    "        JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])        \n",
    "    \n",
    "    S = JH*P*JH.T + R\n",
    "    K = (P*JH.T) * np.linalg.inv(S)\n",
    "\n",
    "    # Update the estimate via\n",
    "    Z = measurements[:,filterstep].reshape(JH.shape[0],1)\n",
    "    y = Z - (hx)                         # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "\n",
    "    # Update the error covariance\n",
    "    P = (I - (K*JH))*P\n",
    "\n",
    "\n",
    "    # Save states for Plotting\n",
    "    x0.append(float(x[0]))\n",
    "    x1.append(float(x[1]))\n",
    "    x2.append(float(x[2]))\n",
    "    x3.append(float(x[3]))\n",
    "    x4.append(float(x[4]))\n",
    "    x5.append(float(x[5]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))    \n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Pdv.append(float(P[5,5]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))\n",
    "    Kdv.append(float(K[5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncertainties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10895ced0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WLVJenteRAACABDJz5zPSyQ97HQYAIAr8kcx26CA1bUpTYwAA4KoUk+p1CACAKPFHMivR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\n8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8msmZmZmZmZVR0ns2ZmZmZmZlZ1nMyamZmZmZlZ1XEya2Zm1oKkjyQtybbFkj4laWH2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\nX00j0NcfENMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e3b610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.semilogy(range(m),Px, label='$x$')\n",
    "plt.step(range(m),Py, label='$y$')\n",
    "plt.step(range(m),Pdx, label='$\\psi$')\n",
    "plt.step(range(m),Pdy, label='$v$')\n",
    "plt.step(range(m),Pddx, label='$\\dot \\psi$')\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bZkkTlCQ1ULcV1Atf+EJe+MIXblj+0pe+NLLJamBey/I8iiqq1Z8A55fHngO8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\nE5QkqZJMUJKkSvr/ZWe/eDYTN/IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083810d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hvfdqv69Xr/RmkdyjYldERERERLy44oq675swAZYuTV8WyT0qduswZozvBCIi\nIiIiue2BB+q/v1On9OSQ3KRitw6HHeY7gYiISHSs9Z1ARPLdqlUNL7NhA6xYEX0Wqe7ll1/mlltu\n4eijj6akpASAiRMn0rZtW6Zk0exhjXwHyGTffw+77+47hYiISPgGDoQBA3ynEJF89vDD8S130UXw\n/PPRZomC+eCDtG3L9u0bWlvz589n7ty53HjjjXTr1o1x48Zx4okn0qFDB4wxfP/99+y5556hbS9K\nKnbr0a0bVFRAgY5/i4iI5IS//73hbpMikh5XXhnfciNGZGexG2YBmk5vv/025557Lt9++y0zZszg\ngAMOAKBjx46cd955dO7c2XPC+KmMa0DXrr4TiIiISFgefNB3AhFJxujRvhPkj9///ve0atWKRx55\nhP79+7PddtttvK9Fixb06NHDY7rEqNhtwMyZ0K6dO9n1738Pa9f6TiQiIiIikt0SPdd3//7R5JDa\nWWt56aWXOPnkk6vdVlFRQWFhocdkiVGxG4fiYigqgscfh+bN3UB5ERERERFJzkcfJb6OJqpKn6VL\nl7JkyRJ69uy58bZ33nmHQw891GOqxKnYTcIWW7ixvCIiIpK7dBpCkegMHpz4OllWZ2W1Vq1a0bRp\nU8rLywFYvnw5H330EX369PGcLDGaoCpJjRrptA0iIiK57NNP9eNaJJN8/TWUlkKTJr6T5L6ioiKe\neeYZ7rjjDvbZZx/Kysq4/vrrfcdKmIrdFOy8M/z4o+8UIiIiIiL54YYb4J57fKfIDyeffHK1MbvZ\nSN2YUzBzJuy0k47wioiIiIjEa9q05Ne991799pb4qdhN0axZ7jy869f7TiIiIpKYYChW/mgz3XcC\nEQGefjq19YcODSWG5AEVuyFp0gSWLvWdQkREJH733ec7QZr1uTmhxcvKIsohkucefTS19W++WUd3\nJT4qdkO0zTbw6qu+U4iIiMRn1izfCdKsMLFzB950U0Q5RPJcGAeICgrgtddSb0dyW8rFrjHmKGPM\n98aY6caYq+tY5u/B/d8YY3rE3D7bGDPJGPOVMWZCqlkywcknQ+vWedg1TERERESkAZWV4bV10knq\ngSH1S6nYNcYUAvcDRwF7AGcYY7rVWOYYYBdrbVdgMPBQzN0W6Gut7WGt3S+VLJlkxQpo3BhOOAEW\nLfKdprrly2H4cDjsMDCm+qVzZ1izxndCERFJF+2YFZF0W7cu3PaKisJtT3JLqkd29wNmWGtnW2vL\ngBHACTWpjnKDAAAgAElEQVSWOR54CsBa+xnQyhizbcz9JsUMGev116FDh03F5J//DGvXpjdDcbEb\nxF+VoU0bl2PMmM2XnTsXWrSAQw6BkpL05hQRkfR75BHfCUQk38ydG36bW26Z/Bje6dN1KtFclmqx\n2xGYF3N9fnBbvMtY4D1jzOfGmPNTzJLxhg+H5s1d0bnHHvD+++EOrl+zBkaMgF69NhW37drBsGGJ\ntTN+PLRtG14uERERERGAyy4Lv81Vq9wY3meeqf7beulSeOEFOO206gegOnVyB3euvRZ23RV22cXd\n/t674WcTvxqluH68pVpdR28PttYuNMZsDbxrjPneWjt+s6XGAAwNrvQNLtlt6lTo12/T9T33dEdc\nTzhhU6E5Zw6ccw588IGPhPDll9Czp59ti4iIROWbb6B79/iWrax0P6JFJByTJ0fX9qBB7tKQBQvc\nZfzmVYekyQcffMAHaShyUi12FwDbx1zfHnfktr5lOgW3Ya1dGPy71BjzKq5b9OZvu0OBsUNTjJrZ\npkyB885zl0zxy19qWncRkVxnrTuikU8+/1zFrogvixf7TiCZoG/fvvTt23fj9WGJdkWNU6pf358D\nXY0xXYwxRcBpwOs1lnkdGARgjDkAWGGtXWKMaWaMaRnc3hw4EohwX48kY+FC3wlERCRKK1b4TiAi\nIhKNlI7sWmvLjTEXA+8AhcDj1tqpxpgLgvsftta+ZYw5xhgzA1gDnBusvh3winG7kxsBz1lrR6eS\nR8K3995ukisREclN6sEjIumi35SSbql2Y8ZaOwoYVeO2h2tcv7iW9WYC+6S6fYlWSQls2KBp3UVE\nJD+tWgWtW/tOIZIb1IVZ0k2jUKRBb7zhO4GIiETlL3/xnSD9Ejmafe210eUQyTeaEErSTcWuNOiU\nU3wnEBGRqIwc6TtB+p2fwMkOZ82KLodIvrnoIt8JJFFvvfUWrVu3ZvTo7BxtqmJX4rJune8EIiIS\nBY3ZFRGRujRq1IgmTZpgsnTa/pTH7Ep+ePppuOAC3ylERCRsCxb4TpDZ1q71nUBExJ8jjzySRYsW\n+Y6RNB3ZlbhceKHvBCIiIun34Ye+E4iISLJU7IqIiMSptBTWr/edInwVFb4TiEiue+st3wkkLLfc\ncovvCHFTsStx095tEclXY8aAMdC0KTRp4v5+8sncGe86dqzvBCKS6775xncCCcOcOXNo37697xhx\nU7Ercbv8ct8JRETS77XX4LDDNr/93HOhoCA3TqWxZo3vBJmtstJ3gk0mTYJ+/dwOF2Ngr73grrtg\n4ULfyUTqd889vhNIGMaPH0+fPn18x4ibil2J2+ef+04gIpJekybBSSfVv8whh8B++6UnT1QefNB3\ngsw2ZYrvBK6reZMm0L07vP/+ptunTIGrr4aOHTcVwJMm+cspUpeSEt8JJAw//PADXbt29R0jbip2\nJSGalVJE8sW6da6wiMfEidCzZ7R5ovT2274TpMleLya1Wnl5yDkSZC00ahT/ePHu3V3R6zu3SJVc\nGfIhYLPsxVSxKwnJhL3bIiLp0KxZYst/9RWMGxdNFgnfDz/4ThC/3XZLbr3GjTOrC7bkL02Cl31G\njRrFLbfcQv/+/SkuLgZgyZIlbLfddgB8/vnntG3blikZXhyo2JWE/OEPvhOIiEQv2f+7+/TRj7ps\nkcj4wTvvjC5HQ/73P5g+Pfn1CwvDyyKSrE8/9Z1AElFSUsKECRO48cYb+fHHHxkX7MkdN24cvXv3\nBtg4SdXUqVO95YxHI98BJLto3K6I5IO99kp+3b/8BW67Lbws6fLTT7DNNr5TpE8iOyVeeAFGjIgu\nS30OPzz1Nh56CC66KPV2RJKVjd+JYfjAfJC2bfW1fUNra/To0QwcOJBp06Yxe/Zs9t9/fwAmT57M\nqaeeCkDHjh0577zz6NKlS2jbjYKKXUlYebkbOyQikos+/ji19f/6V7jpJigqCidPutx/P9x8s+8U\nEuu998Jp5w9/gN/9zr0nZ82CnXYKp12ReOXNvAA1hFmAptPpp58OwHXXXcehhx5Khw4dAKisrMQY\ns3G5li1bss8++3jJGC91Y5aE6XyMuaesDD75BG64AYYMgUWLfCcS8adXr9TbuPrq1NtIt6ee8p0g\nvZ54wneChh1xRHht7bij6521887htSkiuW3kyJEcf/zxACxfvpw2bdpsvK+0tJTmzZvTKMOPgKnY\nlYQ995zvBJKKBQugQ4dNp6gwxu3tP+gg183o3nvd/d27a/ZEyT8//RROO/fdF0476TR3ru8EEmvZ\nsnDbW7Ro09jfdevCbVukPjoHdPaaPXv2xtMMffjhhxvH6wI88MADDBo0yFe0uKnYlYT961++E0gy\nvv7aFbadOsV35HbSJCgocEd9RfLF+eeH19bkyeG1lS4bNvhOIFX69Qu/zYED3b9DhoTftkhdFi/2\nnUCSddBBB/FpMLvYl19+Sc+ePdmwYQN33303/fr1o127dp4TNkzFrkiO27AB2rSBHj2SW7+oKP5z\nO4pku9dfD6+tX/wivLbSZckS3wnSK5HeK19/HV2Omioq4Jtvomv/wQfVc0fS58ILfSdIUqNS3wm8\ne/7555k9ezaDBw9m/PjxPPjggwwfPpyzzjqL7vGeiN6zzO5kLRmrtBSaNPGdQhpSXAxh7HRr0gTW\nrEn8vKMi2SSKH/9lZe5cp9ni0kvh1Vd9p0ifRLpXjh8P6ZqHZcyY6LcxeXJ27pCR7DNxou8ESer5\nGEy42HcKr9q1a8eTTz5JaWkpw4cP55JLLvEdKWE6sitJeegh3wmkIdOmhVPoVmneHJ58Mrz2RDLN\nvHnht/nJJ+G3GaXXXvOdIHOls4dLmBNT1SVLDsqI+NO02HeCjDFx4kR69uzpO0ZSVOxKUp55xncC\nqc+338Luu4ff7rnnunG/J56oCU4k95x7bvht9ukTfptRW7vWd4L0mTkz/mWvvDK6HLHSOU/CypXp\n25bkp/Jy3wkkDJ999tnGc+1mGxW7kpSvvvKdQOryyiuw997RbmPkSNeluWtX/ViS3PG//0XTbraN\njQxz3HKm+93vfCfY3OOPp29b2ThruGSXF17wnUDCsGrVKlq1auU7RlJU7ErStLcu85xxBpxySvq2\nN2MGtGoF+++ffT/oRWLNmBFd2+PHR9d2FM44w3eC9MnEc4pfdFH6tjV0aPq2Jfnps898J5AwDBs2\nzHeEpKnYlaTpFBWZY8EC1714xAg/258wwZ2mSCRb3X57dG1n7UykuSpmhtU1azzmyBDLl/tOILns\nH//wnUDynX6eStL0BebP4sVw+eWuwK06d24m+OtffScQSc4TT0TX9tSp0bUdlaee8p0gQlvNSXrV\nqHs0/fOf0bZfm1tuSf82RUTSRcWuJO2xx3wnyE/HHgvt22fmWKvrr8+vyW0kN6RjQqBs+1ycc47v\nBOlTmsCpNKPsAQDp7cJcZfhw+Oij9G9XRCQdVOxK0qIc4ya1e/NNd8lkgwf7ThC///4Xjj/edwrx\nLR1HMbOxJ8yyZb4TpMd778W/7HffRZdj9ero2m7I3Xf727bkLv1OlEygYldSUlHhO0H+qKhwR3Uz\n3XPPZc/74p13XMFb1R3cGGjZEs48E8aNg5ISjU3PB+efH/02rrkm+m2ErVs33wkyT5TzIvjsOj5y\npL9tS+66+WbfCURU7EqKJkzwnSB/ZFO38Ucf9Z0geatXu4K9Tx9o2xa22KJ6MWxMZs7gKsmprEzf\ntrJtBvtly9wOH0mPiy/2u/1s2Ukp2eOZZ3wnEFGxKykaN853gvyRTTO6+hh3lk4dOriiN8oujZIe\ns2alb1vz56dvW2Fp3953gsyzalX4bSYybjgqkyf7TiAiEj4Vu5KSbOyal41mzvSdIHFR/CAM0xdf\nwAMPpNbGnnu6ovfCC2H9+nBySXoNGJC+bV1ySfq2FZYNG+Dbb32nyCyLF4ff5quvht9mos4+23cC\nySVLl/pOIOKo2BXJAqec4jtB4gYN8p2gdqNGuQJ1333Da/Phh6FJk+pdnXfaCYYOhbfe8jvxjNQv\nnUMx3ngjfdsK0957+06QWaKYJDCdO13qMmmS7wSSS7KxJ0u8jDG6JHjxScWuSIazFr7+2neKxL32\nmsueSe67D445Jj3bmjULhg2DX//aTXoVWwgfdZQrfLLtdDS5Zk7yp1tNWrbOcHz00b4TZI7LL/ed\nIDqzZ/tOILkiV09fZq3VJcmLLyp2JWX//a/vBLktm/eOjh/vO8Emb76ZOT9S33kHjjsOmjffVAC3\nbQunnw7PPpv5XcBzxV13pX+br7yS/m2G4e234fnnfafITZn0eb/uOt8J/Nuwwc93Q65RTwHJFCp2\nJWWvv+47QW477zzfCZLXp4/vBE55eeaftqmkBF54Ac46C7bcclMRfPnlMHVq5h0lzwUPPpj+bV5w\nQfq3GZYBAxI7J23G2nKB7wTV3Hef7wSbaIeGm23/6qt9pxCRsKjYlZRl0ylxstG77/pOkBofXUVr\nyuYxh/fdB3vsAQUFm58CyRho1w4GDnRHDH/80RX21qb3lDrZaOFC3wmy0xFHwIcfJr5eWRk8+SQ0\nalT7+9gYKCra9PdTT0U46dvJA1NuYuLEEHIE/vKX8NoKw5o1vhNItps+3XcCkU1U7EoodNQpGrnw\ng7xLF7/bX7QIvv/eb4YoFRfDv//tJjHbZRdo3NgVxoWFmxcThx8OP//sO3Fm8Hkqr08+8bftMPTu\n7YrReHzxxaZC9txz6z+Xa1nZpr/POaf6pG/bbgvXXgtjxrheGsbArbe69qdPdxPBXXpp3YX0Ht1i\nNtQy9emUP/005SYy1pAhvhNItsukIUwixueA4XgYYyxDgaGZnTPfrV/vfsxIuO64w/3Ay3bz50PH\njn627XkSwIx0/PFuArF8fm58PvZ99oGvvkrPtkpK3HjwKBQVwYoV0LRp9dvLyuCGGzJs3GOzpXDV\nNpuuh/CbIoyfT2vWQIsWqbcTtqrH1rEjzJix+Wucy+bMcTtpM/zncUbL6v9bet8Gh9/g/h4zFMbe\nBOj9kA7GGKy1ob97dGRXQnHLLb4T5KZcKHQBOnXy8x9FLhwZj8Lrr7ujv6WlvpP4sWiR3+1n4+zq\ntdmwAZo1C46c7lG9O3JGFboZbO5c3wlq99hjbrKqhQvhm298p/EjW08VJiHaPsu74QigYldCcuut\nvhNIpisoSH/B67sLdaZr2hTWrfOdIv0yYbKyXDvt1NSpvhNkp4sv9p2gduefD7ff7v7+3e/8ZvHl\nuON8JxDvdnnHdwIJgYpdCY26eIRrwgTfCcJXUFB9XF6U1q5N37ayWbNm7ghdvrAWvvzSdwqd4iUX\nvBPC7+D//S/1NqI2daor/PKxp4zvXiDJeOcdGDzY3ySFX3zhZ7sidVGxK6H57jvfCXLL00/7ThCN\noiJYuTL67ficgCjbbLFF/uys+uEH3wmc//s/3wkkVX/9q+8E6fPGG278br71BOnQwXeCxB11FDz6\nqL/fZPff72e7InVRsSuhUXERrgce8J0gOq1aRT9D8jPPRNt+runa1XeCzc2dC3fe6WacDsugQeG1\nlaowH5ek37hxqa0/bVo4OdLpkUfy77RmPs7Hnah16+Dhh6tPDNWzp58sTz7pZ7sidVGxK6FJ5tyL\nkr+6dYPZs6NpO5dPCxKVH3/MrEmFRo2Czp3hmmvcuYSPOSacdjNpeMBzz/lOIKlK5Zy0mdCdPlF/\n+lP+fb/+8Y+wOPWzVUWmpMQNR6l5wKGsLP1DefJtR4hkBxW7Eqp0nU4j161e7TtBeuy4YzTdZw88\nMPw288HVV8O77/pOAYcdtnlxO2qUuz0VmTYL8mWXhddWRQU8+6zrahp7ftmoTjskzrffJr/ugAHh\n5UinXr3gb3+DPn1g0iTfadKjfXtYtcp3itrNm1f3fek+yrpkSXq3JxIPFbsSql/9yneC3HDbbb4T\npM/554fb3pw54baXb4480t+pRqyFXXaBMWNqv3/MmNS6p2dSF+Yq5eWprV9a6sbBN2oEZ52Vn5MI\n+ZSJ76l0uOIK1407n8ZnbrmlO4qaSWbOdOe0rsvgwenLArk714hkNxW7EqqKitS6dYlzxx2+E6TP\n44+H+57R6YZSt88+fo7YFBW57tT1GTQI5s9Prv3Jk5NbL0pPPJHa+vvuq1nHfcqUCc98efRR3wnS\nq23bzBoK8c47DZ8POJ3v0WuuSd+2ROKlYldC162bv21PmeK6KqZjtl8JT1jncczkcVXZpnt3d57N\ndHXdO/LI+I9ybr994u2PHp34OulwwQXJrWet66Y8ZUq4eSRxDe2gqc0rr4Sfw5c//MH1MMgX+++f\nXeco32033wlE/FKxK6GbNy89Y+OWLnU/xlu33jQ+ba+9oEcPN9tv1W0nnpg9/ymBe1z55sUXYf36\n1Ntp3z71NmST665zXfcuvDDaUxNddVXiY4WPPjqx5fv3T2z5dErmud1yy/BzSHLuvDPxdYYPDz+H\nLw895CZx8mn9evjHPzYfs96jh8s2ciQsXx7e91hpqZsU6swzXY+2TJeOHcHJ7PQRSQcVuxKJHj3C\n39NbXOz2IFf9J7bNNu7H+IoV9a83cqT7T+mww1IfH5cO2ThDZxhS/bGk/2ij8/DDUFAQzalyBg2C\nu+9OfL23345/BvioT3OVqr//PbHlL7ssfyaxywbJdOXNtbMXpNodP1kLFrjfA02awKWXbj5m/euv\n3amDTjwR2rRx32OxxXD//vCvf7md9MnMJPzcc268fPPmmf09k44dwf/5T/TbEEmGil2JTNOmqRWX\n1rqjPe3auf+U2rVze5CTNWYMNG4MN90U7VGqVJ17ru8Efjz+ePLrVk1sJNFq1y687sDr17vPdSoT\nTvXuHd+EZD6HVsTjT3+Kf9lvvkm8OJbo/fxz/Mtu2BBdDp/S3YPqrrugU6fU2hg92g2j2WEHKCx0\n30nJzPuwdq37nqkqou+7z92WSd57L9r2NV5XMpWKXYlU48aJHQ2aMgV23939Z1FQ4MbxhX006eab\nXdsnnJB5MysCLFrkO4E/yXQHBLfnXtKjf3/o1y+1HUZvvOGOxIShS5f6u+i9/HI424naZ581vMza\ntW7yMAlBYbgVZyJjr99+O9RNZ4xWrdK3rb593anSMtXll7ujvVXF79lnw8SJiR0AsHbz79lUvneP\nOCJ3d7SI1EfFrkSuXTs4+ODau91ZC+PHVx9zO21aenK9/rqbWbGqK1MmzCKd77OqXnNN4r0BVqyA\niy+OJo/U7v333Q6j5csTW++nn9zn7bjjws3Tvr2blbSmlSvh1FPD3VZUDjig4WWaN48+R97Y/dVQ\nmxsxIv5lTzgh1E1njA0bYNmy6Ldz4okwdmz02wnT00/Dfvu5AwCx3ajruxQUbN7tOvZ6Mkdqt9jC\n/d4Je6d6JnfhFlGxK2nx0UfQsmXtX+aHHOI7nevK1KIF3HOP3xyjRvndfia48srElm/dOpoc0rA2\nbeDQQxueXKy8HI49FrbdNrosRx3lvlOmTnVj7/797/QeaQrD88/Xfd/BB6cvR14oCn/QczyntsqG\nyYxScf310bZ/771uHg5xR2qTMXo0dOgQ7s713/8+vLZEwqZiVyTGlVe62RV9efhhf9vOFPfd1/Ck\nY1UuuijaLNKwDz5wXZKNgddeq35k/rvv3H2NG8Obb6Ynzx57uLF3AwemZ3thGjCg9qEVV13ldhhK\nZvvFLxpeprYeCLnkkUeiOxvDmDEwZEg0beejoqLw5i/J7e+nDJ7kReKiYlekhueeg6FD/Wz7rbf8\nbDfTxHO09r334J//jD6LxO+kk6p309tzz3BOKZVP2rZ1Y5rBdcNu1Ci52arFj/nz67//+OPTk8On\nHj3qP//z119v+o4455z4xpHOnevOqCDhKihIfSKtlSvDyZKxQh7fL+mnYlekFsOGue6Q4s9VV9V9\n38cfJ9+FSyTTHXecKwRatcr9bq+5Zvvt678/X17PwYNrv33pUlcMV3nqKTeO9OOP625r5Uro3Dnc\nfLJJ7ERasZeXXopv/URmkxfxQcWuSB322CO9pyiaMSN928oGd98NDzyw+e2vvAK9eqU/j4hIPOoa\nu/vvf6c3h08ff7z5sJxZs+DZZ2tfvlcvdyqhmn78MfvG3ueK3/4Wbryx4eWefDLyKCIpUbErUo9E\nTieRqttvT9+2ssXFF7s9zAsWwPTp7u9TTvGdSkSyXo8nImv6F7+o/ZQx2TiOPBUXXlh9/oWddoI/\n/7nu5a++2n3Hv/uuOz2TMTp/um+33gr/+1/d94d13nWRKKnYFanHo4+mbzzKE9H99sp6nTrBrrv6\nTiEiOWOHevrNhqCgoHrBe845kW4uY7Vu7brDGhP/OkceCUcfHV0mSczhh8O6dbXf179/erOIJEPF\nrkgDGhqDFYZ8P7+uiEiuKShw3XkPPNCdZzVf/fa3vhNIqpo127y3wvjxfrKIJErFrkgDVq0K/wTs\nNf30U7Tti4hI+vXqBZ9+6juFSOoOOWTT3xUV1a+LZDIVuyJx6NAh2vYvvjja9kVERESS9eGHrjv6\nY4+5U6KJZAsVuyJxKi6Oru3XXouubREREZEwnH++7wQiiVGxKxKn9u2jaTfVE7qLiIiIiMjmVOyK\nxKmsDB55JPx2X345/DZFRERERPKdil2RBFxwAcyfH26bgwaF256IiIiIhKCg3HcCSZGKXZEE9ezp\nO4GIiIiIRO64C3wnkBSp2BVJ0NKl4Y2zfffdcNoREZEEmUrfCUQk0207yXcCSZGKXZEkHHhgOO0c\neWQ47YiISIIOuM93AhERiZiKXZEkTJoEq1al1kZZWThZREQkCVtP8Z1AREQipmJXJEnt20N5CvMW\nDBsWXhYREREREalOxa5IktasgcaN4fnnE1+3vBxuuy38TCIiIiIi4qjYFUnRgAGJT1g1dGgkUURE\nJF49n/CdQEREIqZiVyQEzZuDtfEtu2KFjuqKiIiIiERNxa5ISLp3b3gZa6F16+iziIiIiIjkOxW7\nIiGZPBmKiuC88+DCC6GyxikcS0uhQJ84ERERkezQtNh3AkmRfnqLhKisDJ54Ah5+GAoLYccd3QRW\nAwZA06a+0wkAncdC96egcL3vJCLiW9MS3wlEJJNtudB3AklRI98BRHLZ7Nmu0JUM0HIBXNFp0/WT\nznH/3rYGypp5iSQinjVa5zuBiIhESEd2RST3FZRXL3RjHXpjerOIiIiISFqo2BWR3HfqaXXf13pW\n+nKISGbZebTvBCIiEiEVuyKS20wl7PFK3fd3exX6XQPbTK79/oIy2HqK6wbd72q4oj10+ByI81xT\nIpK5jrrcdwIREYmQxuyKSG7r8XjDyxx8p7vEa/CvNr9tyqmwcF/Y+jtotgzm9YKl3dx44LkHQ1nz\n+NsXkfQoKPedQEREIqRiV0Ry2/GD07OdPf/jLlV2favuZT+8Gib+AX7uCLYw+mwiUruiNb4TiIhI\nhFTsikjuapmhpwyo60jyD8fAlN/Cd6fqSLCIiIhIilTsikjuOvBe3wkSs+tb7lJ1WiSA2X3gs0tg\nxtE6RZKIiEi6tZkB7OI7hSRJxa6I5K6D/uY7Qeq6jHWX+kw+Hd67E1bukJ5MIrmk/Rew6Je+U4hI\npmpajIrd7KViV0Ryk6n0nSB99h7hLlU+GgLfnwjzD9CYYJGGtJ6pYldEJEep2BWR3LTHfxpeJlf1\nusddYn12MYy7EdZs4yeTSKbqPA6++43vFCIiEgGdZ1dEctORQ3wnyCz73w9XbgvHXOw7iUhm2f9+\n3wlERCQiKnZFJDdtNc93gsy03wMw4FjfKUREREQip27MIiL5Ztc3ofdfYfx1vpNIrmuyAo6+FLo/\nU/cyP/wa3r8NlvwCilbDhpbJb6+gDLb5FtpOh/ImMLcXrGubfHsiIlsu8J1AUqBiV0Ryz47/850g\n8x1+PXx5HqzZ1ncSyUXbfQUX9oxv2V3fdJfaLPylK4annQArukBloSue93k6tKgANF6rU3uJSO1O\nOwWwvlNIklTsikju6TPMd4LscOV2MFT/gUuIWi6EKzqG116HL9yl783htVmbA4bD+Ouj3YaIiKSd\nxuyKSO7pMs53guyx4/u+E0hOsPCb34Rb6KZT8598JxARkQjoyK6I5JYmy30nyC5n94Nh5Tofby5o\n/wUM/DW0WLLptjkHw8gnoKRrdNvd9Q0YcFx07YuIiCRJR3ZFJLdsO8l3guzTJ+IuohKtgjIYauCC\nfasXugCdP4RLdw1/m6bCdf0dalToiohIxtKRXRHJLSef6TtB9ul7M3ygcc5ZqaAc/lKUvu0dMByO\n+nP6ticiIpICFbsiklu2mu87QXY66B74eIjvFJKoA+5Lz3baToNLdk/PtkQSVbMr/fu3wYfXgFUH\nRpF8p28BEckdTVb4TpC9jrwSnVohyxSUB69bxLq9rEJXMpOpqL0r/eHXw02FcMK5YCr9ZBORjKBi\nV0Ryxz5P+k6Q3Xb4yHcCScRRf4p+G3uNgNNOjX47Ism4qYEOij2edEXvXiPSEkdEMo+KXRHJHUdd\n7jtBdvtdb98JNjEV0PuvcF1z6DzWd5rMU1AG+z0Q7TY6TIRTz4h2GyLJOuKq+Jc99Qx3BLjV7Mji\niEhm0phdERHZpPM4mHOI3wxd34SBx266fm5f9++dxbCujZdIGefAv0XbfqN1MHi/aLchkqxmS6HX\n3Ymv96cdobgrPPAdVOonsEg+0JFdEckN237jO0FuOLeP3+13/Kx6oRvr6rbQ/en05slUR1wTbftD\n2kfbvkgqrtom+XXbToe/NIZ+V6N5CkRyn4pdyV5bzYUjh8CNjV33pNhLt1eI+z8xY6Gowv0r2eu3\nv/GdIHd0+NzPdreaC+cfUP8yJ53tPuON16QnUyZqsSja9tt9D01WRrsNkWQ1WxpOOwffBUMLoNed\nqOgVyV3qwyFJstB/MVwzLfymZzaHkiJYWwirGkHxFu56uYG1ldDjFtj6NSj7GSpLa2/jtFPcvy+8\nDPzD5WoAACAASURBVFNPrn5fYSX0WAFDpsG26zdf9x+7wCsdARPqw5JaDJwDv5+16fpjO8Kb7WFF\nXecNtdCkEgotlBkoKwAbvE5tp0ceN28M/hUM9fDj7/LO8S97fQv4+mwY+UT+nV4k6h07F3eLtn2R\nVPzu4HDbO+Iad5k0AF59GmxhuO2LiFcqdiVxXdbAvyZG1/5Oa9ylTmcElzj0Afggse1fMsNdTjgI\nfq6r6JLUWHjxE9h6Q/Wbfz+revGbkDGb37R+GRR/BCu+hhXfQNnyJNuOVQAFjaGwmfsXA7bcXSrL\n3AULptD9i3EXUwgm+JcCKGwKjVpA463cbRXroHKDW6bRlrDF1tBkO/e3Ddo1BZu2gwVbAWWr3L8V\na2D9UrcTqHwVmEZQUOTaL2wKjVpCUSvXXmETaNwKitpAo2ZQ2AKKWkPjLWOezg9CeK7i8NwO8EQX\n2DOJ2VL3ecpdPrwK3ruDvNlBFeWs2W1/iK5tyU9Fq2DLBW6MbMnOpPQ5NRXQLqL36C/+7S4AT4yH\nuSEX1SLihYpdScyZs+G82b5TpMfIj+HsX8Hc5r6T5J4bpm5e6EZhi3bQ4QR3kcw0cK67TP0X/JRk\nGwff5S7v3AOfXBFqvIwTVhfOulyyW7TtS35ottQdga2tMB1WnvzR0x5PpJYrXr/r7ad3i4iELs/6\nfklKbp2cP4Vulacmwi6rfKfILXuthMOTrWokZ3W7Hrr9JbU2+g9x43m3+zqcTJno6Euja9tURNe2\n5I+t5roJpOo6AntTIyhanVzbxw9OPpeI5CUVuxIHC/+aAL2KfQfx49EvYIc6ulW3ngnNlqU3Tzbb\nogL+8ZXvFJKptjkUdr8+9XYu7AHn9CUnJ53ZO4nu3vHa7/7o2pb8ULQqvrH317VMvO3WMxNfR0Ty\nnroxS/0aV8Locb5T+PfURBi4IwzuUv9yq9pDy5iZUp8eDTP7kTdjCetl4e3xvkNIptu2nxtjvfjN\n1NrpMtbNtDq0kpz5/G01N9r2j/5TtO1Lbitcn9gkc+2+h2W7x7/86RqOIiKJ05FdqVu/JSp0Yz03\ny036U5+WNU4JMujI4Ae3gRaLo8uWDZ6McFIzyS27DXGTc4VhaAE5c4R334eia7ugPLq2Jfc1WwY3\nNoGmCUwCmOis39t+m9jyIiJk05HdYxfCFT/AqQe6U9Ekq3EFNKuAFuXQshyalbtTmTQrB4w73yoG\nGlW6o5prgqfIAKUF0LTSnQIn9pysW1TC+gJY3QhWN4aVwb/rC6CRhXbrYbtS2GEtbFvqtltg3al1\nlm0BS5q4fxtVQlGla6/QQoVxF4vbLdE4uL2oErYq25SvqNItU1YAlbhTsRQXuedpbjNYXegeQIsy\n2KocOq6DLcug1QboUApbr4e266F5BbRNw6RB2eyQd+HjE6EsiXNQDmkP5VvAHcuhvGn42aoUWPf+\naFoB6wrh50ZQ4Xm/1pMToPNavxkku+z/PIzr52aaTtX5+8OjE1Jvx7fed0TXdrdXomtbclvXN2Hg\nscmt22Q5lLZueLld30iu/bBt/xEcdiPsGDP7/4odYN5BsLgHLNgPftoL1rYlZ3qUiGS57Cl2rwgm\nOvjPJzDkF65gvPp7V6iKpNNBr8GXF8KqJM4x3Gg93NAMnnkbfuzf8PKNK91OiRblbkdHy3JXxG5V\n5nag7LoKDiiJb9vrCuCMA2BlAqdTarseTlwAv1xePUNpAawvhJWNXXG9qhGsbeSulxS56xUGdl8F\nR+f5EW1J3j5/h6/+mHo7HSfCLqNgxtGpt+VL1Edef3NatO1Lbmo7LflCF+DMo+CxzxpebsBxyW8j\nVUWr4Y/dYKv5td/faq671DaefkMzeOEV+PFI4i5+2/7Q8Kzo//geijVzukg8sqPYbdyq+vV7JvnJ\nIVKl5z/dv7Ofcuc0XTnJnSfVNHLnK239Syhf7c6HWtjUnZO1Yp1bdv1SuOhi+OQYeG14cNTVuuL1\npAXw2zr+Q01V00p47WO4fXcY3UAX0YbOpVw1t0indaHFE9nMlnu47sylIewwOfOY7D6VSI/Hk161\n07JORPStIvnst6fCHi+n1kanCW4W8PpORVToscfZwXdAv2uTX79oLZx11KbrFY1h/HXw3SlQvCtU\nbAEFZW4G+ZPPjP8cwpfs7naaE8dOc5E8lx3F7tZ9fScQqV2Xs5Nf95fAxR7GRF/7PawphI+2rv3+\nQ36CYd+lN5NIXfZ/HsYeGk5bJw2CV58Op610O+7CpFZrXtqcZ+5/hkOx1HlkqW2cP7BFqrSbmnqh\nW2Wfp+Cr39V9/29PCWc7ibpo7/DHCReWQd9h7pKqs44iZ+YjEIlQysWuMeYo4D6gEHjMWntnLcv8\nHTgaWAucY639Kt51AWiybaoxRSTWrVPgop7w/ZbVb1ehK5mowwmwcGTq7XR/Bt74J5Q1AyxtKGFH\nZrEzP7IDc2nHMppQylasZDmtmU5X5rID0+nKItqzmhZYH/M6pnD+24LKOPLu8nbS7WeLgsoCjv/8\neF7b77VoN9R4LQz+JWz9/abb7lgOpa3qXoUN7MY0uvMNHVnAVqykkAoqKaCMxvzENqymBfPpxFx2\nYAEdWUdTP+9FgJ1Hw1khHlE84Tz46lxq3RlTuAF28zReNwsmxKq0lbDNFPhpb99RqmlDMUfwLkcy\nmj6MZWfqPm3UGprxKQfwNkcxjkP4gV1ZQSs05lnCklKxa4wpBO4H+gELgInGmNettVNjljkG2MVa\n29UYsz/wEHBAPOtutP3pqcQUkdo89CXcvRu81d5dHzgHfj/LbyaR2nT9E9e+8BZF5WWs2gJ+3gKW\nNoPiZrCqCNY3gkrjho83LYPWpdB+FXQtgd2WwdEzYKv1VY01jzTqWA7hO/ZgIr/iYw5iOl2ppJ4u\nmvHoMjaccHUd3T36spDaz1wt17Xksrcui7bY3eVtOLOWceHXtIZ7FsJq9127PXO5k6s5gwjPmVzD\nfDoyj+35//buO0yq8n7/+P2Z2cqyuyy9N6UrNSIoCMGGDcWgxmgAWzS2xCS2iJpi/BpNYorlp0Yj\n0Yhdo8ZGVJTYKxZEQEUFFdEFFFjYMs/vjzmLw7LLljkzZ/bM+3VdezGnPeczuw+7c5/ynI/VWz21\nUhtVpCUarPc0SK9qjF7TaFUpV40GjNE3SNN+5H+BI/4pLarnSqlDTvJ/XyHyduVD0qmHBnqLRoEq\nNFs361qd2qLti7RJe+tJ7a0nm7T+5+qi97WT1qmd1qpMHfWlnEwxRRRVjdpqg/JUqSJtVHuVq0Cb\nVaDNKtTmrW1UKUe5amAchIXSoBHSugKp39r435MVDR+rQiuQ7JndsZKWO+dWSJKZ3S7pUEmJgXWa\npLmS5Jx70czamVlXSf2asC2AVDr7vfgXkOFe3f93euycc4Iuo1GT9Iwm6Rn9WP+v3uV3aYau1mla\nqIlND8Gz9k66rnaq0u16QedpV72hJox+i+YZc12Dl5p32iD9bER3nfdsmmtK0FOr1FOrNF4vbJ23\nn+Y3v6HXvK8GPLJz/N/P2kqdNsUDw9N9pG4bpA/K4g+y+Lg0fsDqgzLpm3zF8/X02dJbx0ixhI+l\nnRZLI4O57aBtRVttKNwQyL6bo9J5Tzk4bJZ0/9w07dVpbz2hf2qmuuuzxlf3WVetVletTqqNBoOu\n572r6plZ3zy0CsmG3R6SPkmYXilp9yas00NS9yZsCwAp0/4rafAS6bk9g64EjXl8t920tm1blW3I\n/A+gO3KE7tYRunubeffocP1e5+oVfWf7S1N9GpxnjhYrXzFN16o6YTe77vk7/onjddPeN/nb6KAH\nlHfAKRrymbT3h9KMxdL4DB0RrEZ5+kL7qJseTkn7Byzfft4Pmzim6H07F+mc5W9ruQZIJZ9Ipw3z\nt7gmKvumTPf+8V4d8MsDtDlvc+MbZIKR/5QWz5CWpmbU6nZaq9/pAp2qFD7rO0Ax5chUI8uy34fZ\nwpxr+Q/WzL4naapz7iRv+lhJuzvnzkhY50FJlznnnvWm/yvpXEl9G9vWm++uG/CUAMBvA5fF/13V\nXdqY2qtbgUBEa6SdGrhdbumA9NYSpMTvw4o+UmXCE9h2el+KxqT3+0s1SV5xnuk6fCV18J5WV/vz\nr/09mE39YUfyt0h9Po6/ru97MnCZtCVP+qhPeuuqT251lapycoMuI60KNku9P/G3vyb+H+j4pdR+\n7bfTtQ7+7y7q3rujfzvFdsxMzjnfb9ZO9szuKkm9EqZ7Sds94aDuOj29dXKbsK0k6fyBN2vCW28q\n4pwGlXbToLLukuJXviRGdZOUW12tqpz423KSol6YrzFTTiymmkhk6zZ1t8+JxVQdiSjinMzbJrcm\nPjBIVTSq/KoqVebmbnPXU8Q5xcy2abN23xFv385M0VhMMbN4u5GIrHaZt03U23d9dSW+v8R9ytuu\nxtuuvvdS+56jCf9WR6PK8d5X7T5Vz7aJ7yWxrrrfx8TpxNcmaXl76eVuMVXkRtS+IiZTRHk18Xa6\nR+NHbc2k2mMuZpI5p5hMLhK/B8+5+AhmsYT1IoqvY15hzkkmp1yZKiVFFJNTRBFXo5hFt37zattW\nJCKLxVtw5rbZf+LrTQUF2pKXp+6rV6vbunKVrFsr533vSzdulJzT+rZtt77f0g0bFHVO5cXF9faJ\n+n6mid+32vUSt0lcp27/rLte3deJ/TPx51rf/4H69ll3/o5+9vVtE3Eu/j0329pn664XjcUUicW2\n+X+buM4bXaR3O0tldZ5y1C06TGbxfTjF/585JzmTIt60OaeIiylm8f9zTiaZZC5e95JJUtu1hfq6\nrEJeeXLu2/7lvKdCRbz5Ua9/xCx+OZ4svj9z324rfduPIoo/Bzzmna1L3If07X4iXm+uifdImeI1\nykwxi9TbtiRFTJKLxQsx2+51JOYU8/pVTLbd/s3i7yUa+3b/tT8Xk9va1xOPidb+35K3bY2r0hfV\nS2UupqiLqSYS/zma+3Z7SeoaHaKIIjLvPde+f8nJ2bZ9v3Z/UTPFFP//WZUT1X9HDhear+dKKRKL\nH9DJrZL6fyAVfyM9lmVPLan9Pnzce9v551weD8J/+IXUlPG8WrueK6VVPeK/uyTp+7dL60ulR1rx\nY6j91vvj+Pdkfen2y4o2SpsLMuPAyAHLPtIjA3YOuoy0isSkbp/F+7BfijbGD3KUt5em3ydNfUx6\ndH/pvunfrjOrc0nDDaBFFixYoAULFqR8P8me2c2R9J6kvSV9KuklSUfXM0DV6c65A81snKQ/O+fG\nNWVbb3unp56S+65Pj56A75a1l87ZV/rPAKmqiYdP9u2/rx7/4eOpLSydnJO2bJHWrpVWrZKuuUZ6\n8knpo4+CrqxVmbeLdMUe0htdFQ+aDbh1+q06Zvgx6SsMO7Ty65XqdWWvBpdXXVilnEjyT7o7ZvFi\n3fbFF0m3AyQ6+EFp4kLp3MuDrgRonmt69tSpKzP0mvlW6phbpRNvlPaZL9Uk/NlykycHVlO2yMgz\nu865ajM7XdJjip98u9E5966Znewtv84597CZHWhmyyVtlHTcjrZNph6k3r92le4YJj3RX9qU1/j6\nDXn4mNTcLxQYM6mgQOrWLf51Uz33hDknrVgh3Xab9NvfxsNxFqqx+IAlj+8kPTBIereTmv2Ege/v\nwgjtmaRnSU+5i53uX3K/pt/x7aHwy/e5XGfvebZv+7l58GDCLnz30CHxL6DVKSwMuoLQqkn++Cwy\nRNI/SufcI5IeqTPvujrTpzd12/r8/YorkikxKWsLpJe7S4u6Sp8Wx0cY/KAs/npdgVSRG7+Uj8eB\nNd29R97ry1meVsdM6tdPuuCC+FetDz+U/u//pBtuSOnuv2gT76+bcqX1+dKaIiknJlXkSBvz4v24\ndtnawnhf/7RY+rxt/BEvG3Olyqh36WpE3qXDSnvfn9RnkqKRDLh+DNs5bPBhchenboCP3EhEL4we\nrXGv7WA4WAAAWmgtg9WHTlKXMaeDmaWtwj+Ml349WdqQn6YdZqlUfhgOg5qaanU9P1fjVkpjPpV2\nLpfabY4H1XUF8YMtb3SVFnWRVrfNjnvMEn1z/jdqm9c26DIQoH0XLdJ/164NugyEyTdLpeKBQVcB\nNMs1Awbo1GXLgi4jVKLVUvtyaU3nbedzGXPqZeRlzGHR7yfSCo7kpEX5OeVBl5DxotEcPXjm8xp/\n43g9NCjoajLL2B5jCbrQ/BEj1PO557Sq0p/H8gBa/xZhF4BqcqRvSlapZtIPNPzll/XOpk1Bl4Qk\nZXXYnX2oNHdU0FVkj5/u/lOVFXJUoSnG9RwXdAm++9N+f9JPx/1U5o3Qu7Zirdpf3r5ZbTw588lU\nlIZWaOUee+ix8nJNfbOJD/EEGrPqfqnHYUFXASADRMz09tixWltVpUWt/Pnu2S5rw+5OZ0ofNO9z\nNpJ05dQrgy6hVamcU6m8S5IYBSyDVFxQoYKcgm3mlRWW6evzvlbJZU0bzv+W6beoKI+H4eJb+7dv\nv/XSsspYTJ9u2aIPN2/Wkk2btGjDBj21bp2WVlTsuBGg1vvXEHaBoFWWSx//S4oWSZ0mS237p72E\njuVPSoo/8aEsN1eTyzhR05plZdjtdZa0sp5npyF13jyFsy/NlRvN1b1H3qvD7zw86FKSUnNRjSJW\n/43FxfnFWnvuWpX9vvE/JMcOP9bv0hAieZGI+hYWqm9hob67gw8mzjl9WVWl57/+Wk+uXau/f/S2\nNubwQQaSXJX0wXVS/5ODrePL/0nlL8Yvra5YKbmaZmwckXKLpdwyKa+dlFMi5bSV8tpLeR2knGKp\n8iupar0UyZGibaScEu2z8wEqLeyor2viT9se1KaN1lVX65bVq5VvpsFt2mjRxo0ySXuVlmptdbXe\n3LhRkjSgsFDLKioUlbR3WZke5356NKZ6o5STcPD649ukT+ZJ1XXOoH58S3rr8pR13jWQ/SI1sm6A\nqmOnS/8a4WODaNTE3hP1zHHPBF1GqzX2hrF6+dOXgy6jRWIXxbZetrwjVTVVOzyLvaPADCTjmy3f\n1H91geVKBV2k/E5StECSSTUV8Q9pZlK0MH7mIZIXX57TVuo4QSodnvb30CQr5kp9ZwVdReZaeY/0\n/lXx15OeSt9+P7xRWnWvVBPsfYF+/479oKJCO734om/toX5BDVD1yK67anCbNvq0slJ73jk7fr97\nXsf4gZmajVLFp/FB3zYsk7Z8ofjzG1qPXTvvqjd/zEmadGOAKp8QdNPvyVncZ5mMl056Sfbr1vds\nq5qLapoUdKX4WWx3sdMbn7+hif+YqA2V8aO7dx1xl2YMnZHKMpHlivOL61/gquJn1SpWNr2xlXfF\n/+02TRp4VvLF+emjm6WvnpPGXNfoqlnvuenSHvf51tzwoiLt1a6deufna9eiIu1WUqJlq1/V+BvH\n+7aPZPl9MLF/YaFqJk1S9OmnfW0XwZo7eLBmdu26dbpvYaGWTL9Mg68eHGBVwI5lVdhtf07QFWSf\nh45+KDufqeuzLXO2KP+S1vNMrMo5lS368DSy60h9c/43KagIaNiciXN0ycJL/Gvwswekr56Vxt/t\nX5t+2LBUWniANLHRx9tnt6p10uLfSkMvbNLqE0pL9d8RI5QfafrvvA4ZNAhhxQWpua89YqaaSZMY\n0TYkbho0aJugW2tQRx4bgcyWNdcFflwirW0TdBXZ56CBBwVdQijkRfNUfWF10GU06mfjfiZ3sVNu\nNDfoUoAmm7PXHP8brfxKemY//9tNVmyz9PR3pecOlza8H3Q1meOzh7adXvOk9MntjW82frwWjhrV\nrKCbKcb3HK/YRbHtBg/0U8RMC0fx2IvW7viuXXVct24NLr9lejD31gJNkTX37BZeIG3m83daLT51\nsYZ0GhJ0GaGzeM1izXlyjh547wHVNGvgkqYpzS/V76b8TkcMO0KdizrvcF3nnCprKpUTyVE0EvW9\nFiBdUnqrQL8Tpd7HpK79pnj6u/XOdhc7Oef0eWWlnv/6a727aZOeWbdOz65fr42xWLN306+gQGf0\n6KHpHTuqT0FBo7cyOOe0JRbTl1VV+njLFr32zTdauWWLqpyTk/RlVZWqnFOOmQoiEa2prFR5dbUW\nrl8vkzSupERjiot1eMeOGtymjdrn5irXTLV7bcqtFIfMO0QPLX2o/oU9j5B2OnW72Ud16qR5Q4c2\n+VaN+lz90tU6/ZHTW7x9Mpo6noKfbMGCtO4v7C7p10+98/M1c8mSBtc5p1cvDSsqUofcXDnnVO2c\n5q5erXXV1SqJRvXAV181up++BQX6cFzjVyK0xtutGsI9u8FI1T27WRN27Vc+NIJmcRdndt8KE+ec\n7njnDh19z9EtbmPaoGm676j7GAgKWWnuG3M1+9+zU7eDvPbS+HvqX/bxPH0440r1KCiQk7Sppkbr\nqqu1pqpKn1dWauWWLfq0slJvbNigjzZv1vKKClU0EkRNUv+CAnXIieilhSdIX79d73r8nm4k7Erx\nwcj6n6pIp4k6te9QXd6/vwqjyR/cW7NxjTr/YccHFFMliJ/7llhMpy1dqhs//3yH6+WaqSrDP5um\nUs/8fM3s0kUHdeig7xQXK28HVw1srqnR2xs3Ki8SUZ+CApVEo6pxTjnNvNLgvjVrdPg772w3/zvF\nxXp5zJgmtdGaB9Osi7AbDMJuEkadLL3R8NUXSIEVP1mhPu36BF1GVrrxtRt14oMnNmubZ2Y/o4l9\nJqaoIiDzNTYiuK/yOkoW3TpK6ec//1xd2nZJya7KK8rV4fIO9S7bp/8+mv/D+SnZb2vSaNj1XHvQ\ntTrlO6f4uu+gzoYFeZBjfnm5Tl+2bOszsM/p1Uvn9+6tdrnBXX5X97Nwsme9a5zT5lhMFTU12hiL\naYv35RS/fzBiprbRqEqiUZXk5CiS5rPsDXnx6691/gcfqFd+vn7Xr596FjT9Evf3y9/Xzn/bOYXV\npQ9hNxiMxpwEgm76EXSDc8LoEzRzxEwVXVqkqlhVo+uXn1OuskKeM4rslhvNVdSiKbk1YDuVX259\neeeMO1MWdBtz/MjjA9lva/WDXX/ge5tH73K05r09z/d2M9m+7dvrvd13D7qMbfh9SXfUTEXRqIqi\nUXX0teXU2r2kRE+OHNmibXdqv5PP1QD+CP31iqsaeKoEUmf5GcuDLiHr5UZzVXlhpZ4/4fkG1xne\nZbhqLqoh6AKedB/JP2vcWTpi2BFp3SdariS/nucxJ+nPU//se5tAUP469a9BlwBsJ/Rh97hDg64g\n+3B0L3OM6zku/vzak9/Qnr32lCQdO/xYlZ9TrkWnLOL+XCDBkI7pG1BvcMfB+tP+f0rb/pCZOrXp\nFHQJgG9OGH1C0CUA2wn9ZczzyV1pdfOhNwddAuoxousI/e/4/wVdBpDRzEydizrri41fpHxfi09d\nnPJ9NGZS30lBl9BqpOKsrhTvcyO7jtQbn7+RkvaBdGqTyzM+kXnCf1onM+75zxqzRs4KugQAaLEF\nsxakfB9rzl6T9se+1Kd7cfegS2g17phxR8rafvgHD6esbSDdHjv2saBLALYR6rB719CgK8guF0y8\nIOgSACApqX42+KVTLlXHNq1pyBpIUpei1A0i1q04vaNo7tFrj7TuD9llv532C7oEYBuhDrtn7xt0\nBdllzl5zgi4BAJKWyrN45004L2VtI3V26bxLSttfeNzClLaf6OnZT6dtX8hOfdv1DboEYKtQh90v\nioKuIHvs1WcvFeQ0/XlsAJCpZgydkZJ2l52xLCMuX0bz5UZT+wzYCb0npLT9WtUXVisnEvrhWhCw\nh45u/LnVQLqEOuxW5AVdQfZ4/NjHgy4BAHwRsYjvj9DYpfMu2rn9zr62iXBZf976lLa/Zc4WRSPR\nlO4DkKRhnYcFXQKwVajDLtKjf1l/5efkB10GAPjmjN3P8LW9V3/0qq/tJStqhJ6mStc9iCX5Jbr3\nyHt9bzdiEVVfWK28KGcAkD6/mfyboEsAJIU47P5nQNAVZI+3fvxW0CUAgO9unX6rL+08NespgkYr\nVppfmrZ9TR8yXSO6jPCtvX9//9+quaiGM7pIu5+O+2nQJQCSQhx2rxobdAXZ4fqDr+e5agBC6Zjh\nxyTdxlUHXKXJfScnXwwCc9k+l6V1f6+d/FpS24/pNkYf/uRDuYudpg2a5lNVQPMU5xcHXQIgKcRh\n91HO7KbcLp130UljTgq6DABImfJzylu87fUHX6/Txp7mYzX+aV/YPugSWo3epb3Tur+IRVR1YVWz\ntvnDvn9Q9YXVchc7vfKjVxgNFxnhlZNeCboEILxhF6lVVlDG5csAQq+ssEx3HXFXs7e776j7Mvpg\n4D8O/UfQJWAHciI5jQbe3brvprXnrpW72Onne/ycS5WRccZ0HxN0CQBhF803Z+IclZ/b8rMdANCa\nzBg6o1mXIq/62SodNviw1BXkg1Q/NzZMgnpUT04kR+5ip9dPfl3jeo5TWUGZZgydoYXHLZS72Oml\nk15Su4J2gdQGNNWorqOCLqHZDhpwUNAlwEc8bA1NVpBToDVnr1HbvLZBlwIAafXUrKd0xsNn6KqX\nr2pwnT167aGFxy1UxDiODP+M7DpSz5/wfNBlAC1yz5H3qP9f+wddRqNOGXOK9t95f+3WfTf1KOkR\ndDnwEWE3wwzuOFhT+k5RXjRPL6x6QS+sfCHoknTplEt17oRz+QAHIKv97cC/6Q/7/UHXvHyNHln+\niL6q+Eq9SnrppNEnaerOU7mMFADq6FfWL237Ksgp0PIzlqtHSQ9tqtqkuxffretfvV7PfvJso9te\nMuUSdWjTIQ1VIt1CGXZPPjjoCrbXu7S3du+xu/bstaeGdxmurm27qkdJDxXnFcvMkmo75mJav3m9\n3lnzjh5a+pDuXny33l/7ftI1Tx88XfcceU/S9QFAWOTn5Ous8WfprPFnBV0K0oDLvYHkXXvQtfrx\nf36c0n188Ysv1Kmo09bpNrltNHPETM0cMXOb9TZXb9YLK1/Q3Yvv1q1v3qr1W9arJL9EpQXpSpDe\n6AAAF2ZJREFUe8QY0succ0HXsENm1uwKTz5Yuv47KSmnyW6adpNmj5ydkUHROadNVZv04qoXdcVz\nV+jR5Y9uXXbUsKM0ofcEzRwxUyX5JQFWCQBIVnlFuTpcvv3ZitW/WK3ORZ0DqCjzHDLvED209KF6\nl1065VKdP/H8NFcEhEtVTZXyLknds8arL6zmypoQMDM553wPTqE8s/tRgAdnlpy2RIM6DgqugCYw\nMxXlFWlKvyma0m9K0OUAANKMoAsgXXKjuRrTbYxe/exVX9sd1mmYXj7pZYIudiiUN2E+luZn7I7p\nNmbr8P+ZHnQBAEDTMNox4I8nZj7he5tvn/q2CnMLfW8X4RLKM7vpcuFeF+rXk3+dkZcqAwCA5Bw3\n6rigSwBCwe97YpedsczX9hBeoTyzm2rfG/I9VV9Yrd989zcEXQAAQqogpyDoEoDQuGzvy3xp58RR\nJ2rn9jv70hbCj7DbBHcdcZdqLqrRo8c8qqoLq3T3kXdzfwAAAADQRH6MYv/D4T/UDdNu8KEaZAsu\nY96Bp2Y9pcl9J2+d3n/n/YMrBgAAAGil8qLJj8g897C5PlSCbMKZ3QYsOW3JNkEXAAAAQMtde9C1\nLd72gzM/4PZBNBthtx5T+k1hVGUAQChNGzQt6BIAZKljhx/bou127byr+pX187kaZIPQhd2/7J58\nGw8e/WDyjQAAkIF4nA6AoLTNa9ui7V750Ss+V4JsEbqwe/2Y5LbPjeSqTW4bf4oBAAAAsNUNhzRv\ngKkXT3zRl/t9kZ1CF3aT9eqPXg26BAAAACCUZo6Y2eR1J/aeqLE9xqawGoQdYbeOXbvsGnQJAAAg\nYFcfeHXQJQCh1JyztE/PfjqFlSAbEHYTjOgyIugSAABABuhR3CPoEoDQuuuIuxpd593T3mX0ZSQt\ndGF3RRLjbtz//fv9KwQAAADAdmYMnbHD5SeNPkmDOw5OUzUIs9CF3U1J3L/ep7SPf4UAAJCB8qP5\nQZcAADpy2JENLrvu4OvSWAnCLHRht6XyonlcKgEACL1fTvxl0CUAgG4+9OZ653/288/4TA7fEHY9\n8743L+gSAABIub7t+gZdQqswsMPAoEsAQq0wt1DPHv/sNvNuO/w2dW3bNaCKEEaEXc/0wdODLgEA\nAGSIIZ2GBF0CEHp79NpD75/5vk4Zc4o++/lnOnrXo4MuCSGTE3QBmYL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urnh/qlXbt+rO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\nYRcAAAAAEDr/H7u+LwnpGUolAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e26510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.step(range(len(measurements[0])),Kx, label='$x$')\n",
    "plt.step(range(len(measurements[0])),Ky, label='$y$')\n",
    "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n",
    "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n",
    "\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(prop={'size':18})\n",
    "plt.ylim([-0.1,0.1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2VFQUUVFR5QjPGGNMdaIK27bB11/D99/D8uUQFwft20PnzhASAvn5kJcHubk//5mXB9nZ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+hHzE9HOLSnEidOwPHjkJzsSoxr1IDatSEqClq0gMaNoVEjiIy89NtkikKrVjB3rutnXmOWjKFe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s0lpfjfQncZQa+0KOUmpg46azga3AUqRPiaOTBZyslApp7AtnYxQLlD4lOsoVn3WfNHOsSzCK\neYkuprFw1j3AJK11XZNdbu9TFhe+Dq/RWtuVUtOB5RiVFudrrbd7OSzhu04DrgI2K6U2Nm57APgX\n8IFS6nogE7gMQGu9TSn1AcaXCDtwk/5tAfCbgLeAEIwKsl946kUIn3Wgb0h/Eh1xC/Cfxou96cC1\nGJ9v0qdEu2mt1ymlPgI2YPSRDcCrQDjSp0QbKaUWAmcAsUqpHOARXPtZNx94Rym1GyjGuNgsOrFm\n+tQ/ML6TBwIrGotOf6+1vskTfUr9djwhhBBCCCGEEKLr6SxDqYUQQgghhBBCiKMiibEQQgghhBBC\niC5NEmMhhBBCCCGEEF2aJMZCCCGEEEIIIbo0SYyFEEIIIYQQQnRpkhgLIYQQQgghhOjSJDEWQggh\nhBBCCNGlSWIshBBCCCGEEKJLk8RYCCGEEEIIIUSXJomxEEIIIYQQQoguTRJjIYQQQgghhBBdmiTG\nQgghhBBCCCG6NJ9JjJVS45VSO5RSu5VS9x2hzTil1Eal1BalVKqHQxRCCCGEEEII0QkprbW3Y0Ap\nZQZ2AmcDucBPwBVa6+1N2kQBa4DztNZ7lVKxWusirwQshBBCCCGEEKLT8JU7xicCaVrrTK21DXgP\nmHRYmz8DH2ut9wJIUiyEEEIIIYQQwhV8JTFOAnKaPN7buK2pAUCMUmq1Umq9Uupqj0UnhBBCCCGE\nEKLTsng7gEZtGc8dABwH/AEIBb5XSv2gtd7t1siEEEIIIYQQQnRqvpIY5wLJTR4nY9w1bioHKNJa\n1wK1SqlvgJHAIYmxUsr7k6aFEEIIIYQQQriN1lq58ni+khivBwYopfoA+4DLgSsOa/MJ8FJjoa4g\n4CTg2eYO5gsFxUTnMXPmTGbOnOntMEQnIf1JuJr0KeFq0qdEWzzx7RM8+HQmaLjzT+N45q+Hf3X/\njfQp4WpKuTQnBnxkjrHW2g5MB5YD24D3tdbblVJTlVJTG9vsAL4ANgM/Aq9prbd5K2YhhBBCCCG6\nolpbLet2Z4KGY4+Fl5amejskITrMJxJjAK31Mq31krK/kQAAIABJREFUIK11f631E43b5mmt5zVp\nM1trPUxrPUJr/aL3ohVCCCGEEKJrKqktYcMGODN+CsefAA0NcN17d+PUTm+HJsRR85nEWAhfNW7c\nOG+HIDoR6U/C1aRPCVeTPiVaU9VQRX6OlYevOpNXLniJiEh48z+VrP25vNn20qeEP5DEWIhWyJu5\ncCXpT8LVpE8JV5M+JVrzzNpnqXdWM3o0BJgDOP98Y/vmHdXNtpc+JfyBJMZCCCGEEB3U4GggvSTd\n22EI4RFVVcbfERHG389eOJMhvWPZsqv5xFgIfyCJsRBCCCFEB3207SOeWvMU+VX5rN+3nvK65oeU\nCtEZVFaaiDMPPPi4e3h3EmMiyNhb5cWohOgYX1muSQghhBDCb8WFxpP6NYxd/Qhnnmlsm3fhvJaf\nJIQfKqsro6DQSVLteYdsT4g3sTs9FxjtncCE6CC5YyyEEEII0UEbdhayayfs3pDElq2w6H/ejkgI\n96i311NWBseOPDSNCA8OYX/1Xi9FJUTHSWIshBBCCNFB+/aa6GkeDdYCfloHRYWQne3tqIRwPYd2\n4HRCXM9DpwuM7j2Esv3dvBSVEB0nibEQQgghRAcVVJaQHJFMt3gbNpuxbf2mGu8GJYQbVNRXUFEO\nEdbAQ7YndTdTU+tAay8FJkQHSWIshBBCCNEBWwq2sLnwF3pExtOzp7EtsVsY29OkQq/ofOxOO2Xl\ncPLAAYds31u3E3p/TXGxlwITooOk+JYQQgghRAf8+8d/U1UJJwzsR0xf6NMHsreHsDPN5u3QhHC5\n6lo7DVnHcspxEYdsP6XnyVgsG8jJgdhYLwUnRAfIHWMhhBBCiA7avx+G9Yvkb8ddz+yL78EaV8ju\nqg3eDksIl9tbUkSI1YHVeuj2XpG9iIqG7GwZSy38k9wxFkIIIYTogPoGsNlg7FhFZOSJAAQEQnrQ\nUmCid4MTwsXKKzTOqt8X2YoKjiIoCPKL64AQzwcmRAfJHWMhhBBCiA7YtyuBpIgkIiN/2zah70Xs\n3w9fpaV6LS4h3CG7OI/IyN+nEEopIsJhe2apF6ISouMkMRainaoaqli0fRF3LXsALaUXhRCiyyss\nUJzTfcoh2wb3M+6YPf/VQm+EJITb2O2KhNDEZveFBIRQXlvl4YiEcA0ZSi1EO+SU53D7olksXw7V\n1XCaKmbyeKkwIYQQXZlSJoYNCDtkW0BwAwCffQZM80JQQrhJVn4pdTV9m92XaO3Btt0FwEDPBiWE\nC8gdYyHaYdY3s9iw0UiK4xNgyXdp3g5JCCGEF9Xb68mr2ofZZD5ku1M7OW+8l4ISwo1sThv9+zZ/\nb21A90Sq5Iax8FOSGAvRRiW1JdTWQmYGLP7bXMb0OpX8Aoe3wxJCCOFFGWUZOJzQv9ehJXpHxI+g\nV7Lxc3m5FwITwk2KiyFIRTS7zxpqosiW4+GIhHANn0mMlVLjlVI7lFK7lVL3tdDuBKWUXSk12ZPx\nCbG3Yi/vvGP8PGGCIirSwq/mt3nlp1e8G5gQQgivqbXVUpLVncSYQ4dSJ0cmExZkxWSG9HQvBSeE\nGzhxEB9rbnZf/x5xFBbbPRyREK7hE4mxUsoMvASMB4YCVyilhhyh3ZPAF4DyaJCiy8sp2wfA2LEQ\nGAjx8ZrcvTBz7iYA7E47tbZab4YohBDCwyrqarCXxzNo0O/3PXPuM8REm9i6zen5wIRwk4KKUqKj\nmk8h+iVF4gwq9nBEQriGrxTfOhFI01pnAiil3gMmAdsPa3cL8BFwgkejEwL47/qlKBM8/KdLADhh\naAIAhQXwwdof+Kr4TZxOeH3SPG+GKYQQwoPmrn0bEiCimZGlSimiop38WvgLcJzHYxPC1ZzaSbUu\nJjworNn94SHBYG7AZoOAAA8HJ0QH+cQdYyAJaDohYW/jtoOUUkkYyfKcxk2yTo7wqKC63iQVXcM5\n/c4BICrCzJVXQUpfuPyJN1m6BN56y7sxCiGE8KzaWohj2BH3m82QVySjiUTnkF6Sjs0GKUmhze6P\nDI7AFLmPvDwPByaEC/hKYtyWJPd54H5tLByrkKHUwsOKSpz0S4g/+Hhw7GBO7DOMc86GpCTIywOH\nTKsRQoguJbCuFz0qJh1x/6CokZid1iPuF8Kf2J12KsohPLj5Ph0dHE1oiJnqag8HJoQL+MpQ6lwg\nucnjZIy7xk2NBt5TSgHEAhOUUjat9ZLDDzZz5syDP48bN45x48a5OFzRFRVWlpAc+9u4oB7hPbj1\npFsBuCz9GT7M3QXVCd4KTwghhBfsLy2lb58jf50yocjKkRUMROdQY6tBl6bQN6X5e2sWkwWzGbKz\nYfBgDwcnOrXU1FRSU1Pdeg5fSYzXAwOUUn2AfcDlwBVNG2itD64krpR6E1jaXFIMhybGQrhKWXUt\nYxIjm92XODCbi6yw5J1gnE4w+cpYDCGEEG5V3VDN8Jgj3xGOjII8yz6M6/tC+DeHdlCZF0d8fPP7\nA8wBhHerwmZ34jsDU0VncPjNzkcffdTl5/CJHqu1tgPTgeXANuB9rfV2pdRUpdRU70YnhKGqwsyg\nfoHN7rvntLs5Y/hgCKykosLDgQkhhPCaqvJAYqOCj7g/ITyWwgpZyFh0DpmF+WCyExvb/P5gi/G7\nkJ5p82BUQriGTyTGAFrrZVrrQVrr/lrrJxq3zdNa/67Er9b6Wq31Is9HKbqqyvpK6p21xMUENbs/\nOTKZq465EktECfeuuId6e72HI3Sf1RmrO9XrEUIIV9Fa4zDVMWjAkQfgdY+Io7rKZ75uCdEhhWW1\ndAvqgWqh0k9osAWbo8FzQQnhIvJOLUQbFNYUUpEXQ4/EI3/5CbGEoIDX3q7goXcWey44NyqtLWXh\nlvf4MfdHb4cihBA+p9pWTWkJmJX5iG2SepjIC/qa97e878HIhHCPnLxq6utaTh+sQUGUN5R5KCIh\nXEcSYyHaYH/lfurtNvr0OXIbs8mMrXHk0MYtNR6Jy90yyzJ57VX4dkXzc6uFEKIrq6yvJFBZ6dv3\nyLfPwqONETf/fHeVp8ISwm1sds2Q3t1abBPijCczS5bpEP5HEmMh2mD+z29DYCVRUUduY1Zm+vYz\nfi7I6BzVqRf89DEA2VnyViGEEIertdeiG0IJan6WDQA7i7dhMkNurufiEsJdikocmFoYIQEQEl5P\nvbnYQxEJ4TrybVeINkgOOBZVNJyAgCO3CTQHcvYf4I9/hC1l32PvBBdLM3NrAdi5t9DLkQghhO9x\nOB0UZEe1mBhrNOedBxH1QzwXmBBuUmYrxGrVLbaJD03sFN+BRNcjibEQbZBXUkVywMgW2zSusU2P\n7gFgLeCbtXWeCM2t9ufboXAodarE26EIIYTPcWgHQYEmEhOP3GZsr7EEBkB5SQvZsxB+orxc07Nb\nTIttlNNCZpbTQxEJ4TqSGAvRBlUVFuJC49rUtk9kb3r0gJXf+/ddVofTQVlVHYnWnuTmtnx1WAgh\nuqLyunLq63WLd4yHxQ8jJBQsR67dKITfsNs1AaYWhs8B8fFmzAEOD0UkhOtIYixEG+SWFNM7uW3f\naiYPmUy3bvDzbv+eUNbgaKC6LJgThkcTGCwfcEIIcbjKKifYgwk+8jLGBFuCmTTgUkpqZc6l8H9l\nzhz6JltbbBNoUdSrUg9FJITrSGIsRBvUO2uJsrb8QQAw78J59IvpxzHdh5JWlOn+wNyo2lZNTb2N\n3skW8ov9f1i4EEK4WnWtg/CgCEytfJsanZICTjNaBt8IP6a1prISIgNarkptMVvIz5fOLvyPJMZC\ntEFZuZ1eia0nxgcMTupJVY1/V56obqimsiiSlL6aGqdc+RVCiMNVVDlw2luu0AsQYDFjMnFwST8h\n/JFDO9BOM926HXl5MoDkuGjqdJWHohLCdSQxFqIVTu2kQdcRGRra5ucM792D/HL/TibL6spw1IQz\nrG8M2iGT44QQ4nB7i4sJDmn9zphJmXBqJ5WVHghKCDept9dTXesgNrbldsFBYAqWzi78jyTGQrTC\n7rRjrw+gV8+Wi0001SMhECx11PnxCOTymnp0vZXEeDOYHJSXezsiIYTwLQ67IiG69dFEJmUi0FpL\niRT4F36s2lZNQ3UI4eEtt4sPi6WsrOW7ykL4IkmMhWhFnb2O8ipbi2sYH65baBSm0Ao2bXJfXO6W\nVbwfi7YSFGjCGl1Nba23IxJCCN9SWWPH4gxrtV2gOZDQ2EIZSi38msPpwNQQRUJCy+26xZjROHDK\nik3Cz0hiLEQrqhuqCdBhJCe3/TnWQCsxyQWkpvpv8YmSYhOmmgQCzYHYzWUUFXk7IiGE8C25JUUo\nU+vv89YAKxYdKomx8Gu19loqKp1ERrbcLtBiwhxWLP1d+B1JjIVohUM7KMuLbHGdysNFBEWQmAA/\n5qe6LS53KyiromePAKKCowgOr6WiwtsRCSGEb3FqTe+EqFbbmU1m6hocZGd7ICgh3CSnbB/Yg4lq\npcsHW4JxaId8bxB+RxJjIVphd9qxN1hISmr7c0IDQomMgu2VP7gvMDcrKKsiKEgRERRBSJiNujr/\nvfsthBDuUFRWT7ClhUWMG5mVmZj4epxOeR8V/qu0sg6qElCtTB8ODQglJFhRLEt3Cz8jibEQrSip\nLQFLLcGtf/c5xEmx52Kp7O+eoDwgt6yAPgkxWEwWnA4TaenyhU4IIZqqdBQQZGm9ar/FZMFsgqp6\nKdYg/FdhSQOhpphW25lNZsIjndTXeyAoIVxIEmMhWlFWrqEiuV3FtwC6R0WTX+BwT1AeUNfgINwU\nB0BMNDjx73WZhRDClZzaSXFNCf2SWh9KrZRC2cNI3+O/nwlCZBYVEBHRekUtkzJhM5eQm+uBoIRw\nIZ9JjJVS45VSO5RSu5VS9zWz/0ql1Cal1Gal1Bql1DHeiFN0PdkleUTFOFodOnS4hHgzNrv/fgkq\nrCwhpVcgAFo52ZYuk4WEEOKAens9DTaIDIpuU/voKDMOKdMr/FhdtYUIc3yr7cIDwwmJrKGhwQNB\nCeFCPpEYK6XMwEvAeGAocIVSashhzfYAp2utjwEeA171bJSiqyovUzjKE9v9vKAgJzWq0A0ReUad\nvZaIIKP0ZEJIDxzIJ5wQQhxQVFNEbbWJASltm2djUrBzt/9eLBWioMhBYnzrUweCLcEEBUJengeC\nEsKFfCIxBk4E0rTWmVprG/AeMKlpA63191rr8saHPwI9PRyj6KIyS7OJ7db+X5WUxG401Cu0H07N\n1VpTUQn9+xiluANC6sktkSoaQghxQFVDFbaSJMLD29Y+JKqcX2IfwKnlrrHwT/vrd2G1tt7OYrJg\nMkFxRY37gxLChXwlMU4Ccpo83tu47UiuBz53a0RCNMosKCIysG1D5ZoKCwkApan1w1orxbXG+oNx\n3cwARJmTqKiUL3NCCHGA3WmnsjCSHj3a1t5kgswMsDlkcVfhn0rKbQyI69NqO6UUcRGRFJXKSDPh\nX1ofD+EZbb6nppQ6E7gOOO1IbWbOnHnw53HjxjFu3LgOhCa6unqbg56R7VirqZFSioDIQrKyYMjh\nEwN8XHldOVX5scTFGROr47qZ2W8q83JUQgjhOyrqK7DbFcnJbWtvsUB9PWTvdTCgj1tDE8ItanU5\nESFtuGUMoBzkFlYBrRenE6ItUlNTSU1Ndes5fCUxzgWafrQkY9w1PkRjwa3XgPFa69IjHaxpYixE\nR+0tzWOkNbTdz4sIiiA0zElamv8lxrX2WmwVMfTqZTy2mALILjjir5wQQnQ55VV2cAQQFNS29gcS\n6PQMuyTGwi9VVpjoOzSsTW0TY8Io+NUPh8wJn3X4zc5HH33U5efwlaHU64EBSqk+SqlA4HJgSdMG\nSqlewCLgKq11mhdiFF2Q1pr6BicjB7Z/KLVCER3bwNatbgjMzfaVloI2H5xLNLhHEnaHH06WFkII\nNykoqSXM0vbPhoAAiE+A3dnlrTcWwsfU2+ux2Z1trrkSERxBUY3UJhH+xScSY621HZgOLAe2Ae9r\nrbcrpaYqpaY2NnsEiAbmKKU2KqXWeSlc0YXU2muprYPQwLZVHW0qIiiCqPgqtuVmuyEy98raX0mI\nMx6zMcWY0GAzdQ2yjrEQQhywt7iYoOD2XTCMiICyCqnXIPxPbmUuRfmBJLZxkY6esZEUVskULOFf\n2j2UWikVCiRrrXe6MhCt9TJg2WHb5jX5+W/A31x5TiFaU2urxVYbREpK+59rDbQSEADrgh8H5rXa\n3pfkF9cRHmY++Dg0zElZg/8uPSWEEK5WW2PGSutruh6QEp2CUhkUFcuSTcL/lNaWEtTQ/eAUq9Yk\nREdQVlPp3qCEcLF23TFWSl0EbMS4s4tSapRSaknLzxLCf1U1VFFdHtym5QmaY7WCOXucK0PyiD35\nRSSGxx183Cc+FoXyYkRCCOFb6m12EuPNrTdsNCxuGJERUGOTeZfC/9TU26gtTCQysm3tk7vF0BAg\nCxkL/9LeodQzgZOAUgCt9Uagr4tjEsJnOLQDR2U3ktpflBqAsQkX0GDzv7m5FZU2ukWEHHwcEhiA\nttT45dJTQgjhDlnF+zGZ2/7+PnHgRKJUCmmZsrar8D/peYUok5PgNs4s6xMXB9pMpdw0Fn6kvYmx\nTWt9+IQBmSwjOi27005NtZm4uNbbNicqwkxecS1a+1dynFWeRVxk+MHHAaYAzOElFMpoaiGEMDiC\nsKpubW6ulKJvQhz1Df71eSAEQFkpRAW2vb8HWMyYIwooKnJjUEK4WHsT461KqSsBi1JqgFLq38Ba\nN8QlhE8ori4Dk43w8NbbNmdQnyiqItbx+qpVrg3MzQoqyhneq+fBx5HBkYRbA6ir82JQQgjhQxrs\nDnoktn0oNUBwoJl9hXLHWPifnXsLCAsNaHP7mJAYQqIqKZbC1MKPtDcxvgUYBtQDC4EK4HZXByWE\nrygqdkJtDOoop9fGRBlfmj5c5D8ZZZ29jqpKGDHgt4lEFpOFBlVGtv8V2BZCCLcoLG7ApNqXGMfG\nQlFlhZsiEsJ9bHYnA3q2fXmyyKBIQiKr5HuD8CvtTYzP11o/qLU+vvHPQ8CF7ghMCF9QWW0nMTak\n9YZHEGC2cPwJUF/vEyujtUlRTRGlhcGkpPx2NSAsMIyY+FrssmKTEEIAUGPOIzamfYt7DOkVT7Wt\nCocUphZ+Jq1gHyYC29w+NCCU4CBFTY1MHRD+o73f1h9s4zYhOoU9eYU4nEc/jT4yKBKrFcrK/Wcq\n/tb9u9E1MQwd+tu2YEswJmVi/37vxSWEEL5E2UNJjI5o13MirAEQWMXevW4KSgh3cVgYmNT2gitK\nKYJDNNvSZOqA8B9tutSplJoAnA8kKaVehIPrtoQDNjfFJoTXldVUExN8lJW3MObYhIdBWlW5C6Ny\nr3lrPsCi+xLQZCqRSZkwWZxU1dg5iuXPhRCi0ykqdkCf9g2ljggOJ2zgz2RlQe/ebgpMCDfYW76P\n47u1fY4xGN+BiiuqgaNc87IFdqcdh9NBkCXI5ccWXVdb7xjvA34G6hr/PvBnCXCee0ITwvtyC6qJ\niTj6N91uod04t/ckKvxonaPq/Hj6B5z+u+2RYRb27POfBN9bnNp/RgcIIY6eDiqnX9/2JcbD4oYR\nGgJbd/pP3QkhtNbUNdgZNSi+Xc8LDnGwJ8/1Zann/DSHGz65mVs+ecDlxxZdW5sSY631Jq31W0B/\nrfUCrfVbjX8Waa1L3RuiEN6TV1lIrLXtyxM0p29iHDU1/pMsZRTmcdqI5N9tD1LhlNVUeSGi9nNq\nJ2klaR4/b1VDFTd+eqPHzyuE8CyndlJV5STK2r47YeFB4cTHhJBZIGvYCP9RY6uhtg4irO0bMdYv\nLpmdWa69oL4qYxVzF//Cm2/Aa29VU1Li0sOLLq69c4z7KKU+UkptU0plNP7Z45bIhPAB+ZWF9OoW\n26FjxHWz4Ags8YvCVXannbIyOHl44u/2xUWHkJvvH3e+3970Drd/+DSeXj7a5nDtzJID61+nl6Tj\ncDZfrcfmsLHglwUuPa8QHVHdUO13a7e317bCbdQ3QGxM++4YA1hN3Sit8o/3UiEAthdtp7oKevVq\n3xIdPRODKakrdGksb6x7n82bYeAgCAyEr1bLjE7hOu1NjN8E5gJ2YBywAPiPi2MSwicU1RRRUFLH\nyAFHP8cYIDw4GCz1FLr2s8EtyurKKCyCkcf8/q0hOiiGymrfz+43529mxbosPvsUFnzgnQUUP9v1\nGbO+mcV/f/0vT3z7xFEfZ9qn06isr+SpNU+xq3hXs21mps5kbY4sJy98x53L7+SXvF+8HYZb5VXm\nU1eQRPfu7X9uYoyVjH1lrg9KCDepaqiivr798+J7JoRQHb7RpbHs2gV9rSPZ8fRckrpb+HF7jkuP\nL7q29ibGIVrrrwCltc7SWs8ELnB9WEJ433fZ31FcDMcfG9yh44QHhROamMuSVN8vQ/r1nu9Bw/Dh\nv98XHa3ILvT9MUsvr3uZjWm5ACz8eoPHzvtN1jdklxsLNi7ZuYSc8hy+zvyazLJMUjNT2328A8dq\ncDQAxt385hTVuGZI5r7KfS45juja6uzG3NnSus49y6qwpAFK+hN7FAOKwoKDqGlocH1QQrhJbbUF\nioYQ0b4i7IxMGgTh+112Y0BrTd5+uPzYi1BK0TOsL4XVMi1BuE57E+M6pZQZSFNKTVdKTcYdpeaE\n8AENtUGQc+ohyxYdjWBLMElJ8Mjyp1wTmBu9ueZTLAEQ0szSzYmxIRTW5nk+qHbavBm2b4f42AB2\n7Xdvsqe1Pjhk9D+b/8MnOz9ptt3CXxe2eIytBVsPPs4qy2JF+gq2FW77XduimiLyq/IPee4Be0qP\nflbL7uLdPJr6KDU2WVZDHJ3K+kr+sfofZJRmkJYG63fkt/4kD3h709t8k/WNy4+7Yfc+Iq1Ht8Z9\nUrdodmbJHWPhP9Jyygl2xGFqZ9bQMzKJQBXKHhdNuqyz11FcAqeN6AlAt4hQdu+RodTCddqbGN8O\nhAK3AscDVwF/cXVQQrhbcU0xVQ0tF5LasKOIyMBYgjq4EkCwJZiRI6GgpL5jB3Izp3ayZw+MtFza\n7P4RvXphsztwND/V1Wdk50BYGDxw2Xgysxs6PM94T+ke/rf9f83um/bpNN7Z/M7BStQH7uqWV8Di\nxbB7N7R2+tK6Ul788cWDj1dmrOSjbR8dPKZuPMJL617iqTVP8fwPzx8816NfP4oG0vfAE98+eVSv\n7/0t7zN77exD4vcFhdWFMnfaj7y/9QO+3ZjH7O+eZ9UqePzdVLLLs484N95Tlm9bwzNfun7GV1mp\nmT7dfl+LoS16JFqoqfftz4POZEfRDj7Y+oG3w/id+Rvm89muz7jq/ak89dVr3g6nRXvzGkiMb/9S\njRFBEUTHV5OV5Zo4Fmx6m5pqGDXKeNwvKVLuGAuXaldirLVep7Wu1FrnaK3/ClwK9HNLZC7k1E6K\naoqobqj2dijCR8xYNYNXf361xTYFhXZ6J3V8fTxrgJUwK6DB6cPFqWtttezNgWvG/KHZ/RGhgRCW\nT44PT+cprimmsgLmXjaLk4bHQo/1fP1Nx/7Rf9z7I1+kfQEYd8UOtyZ7zcEv/wfu5r7/HhQUGHev\nX3sVsrKMYj0/7P3h4PO+zvyaJ759gge+an65iQPHfGjlQwe3ldeVU1JrDGfPKM1gf+V+Nm2ClV9B\n+VEW/lyVsYqt22DrNg7eMT5wDm/QWjN16VS+yfrGL+dOd8XlurTWLP5pHatXwxtvGNsqKqD3VY8z\n8yPXJSRLdi4hvSSdVRmreGbtM6xIX9HiVAKndvLVV7BkCezc49rP/8ySvcTGtq8Q0QF9u0dTa85r\n80W7WlstU5dO5fuc74/qfF3dS+teYuWele363WytrSt+z1dsX8erXy/hP+/CfS+sx5dH16/O+YL4\nyKh2Py/EEkJwCGRkueau7urtxvSoA3P7o8IDqazy8av1wq+0KTFWSkUqpR5USr2slDpXKWVSSt0C\npAOXuyIQpdR4pdQOpdRupdR9R2jzYuP+TUqpUUc6VlpJ2sG7gcU1xUxdeiM3ffwQt3w0yxWhek1+\nVb5P3dHxpBpbDVOXTmVN9hqXHK+61smvOdktttlXWkpSt/Z/EBxOKcU//vAAVCe0KXnZUbTDZfNG\n26OktpTKCjMTJzb/ZS/eGk9krxy2/X6Er88ori2mqiCe44fG0TuqF0lJsGTt9g4d06R+e5u8+8u7\nqayvZF/lPn7K/eng9ryqPPbmQu4+4+7tAZWNefTy5fCv1Bd4c+ObgHFndlP+JjLLMgHjrnJ1QzWp\nmakU1xgFww7/4rVrN+xvMpLdoY0vA+t+NB5/+mnrr8XutDf7HrLmO+PPU2ueYmvBVh746oFDzr9x\n/0a3VBlel7uOguoCnNrJ/sr9vPbzayxPXw7A6szVAJTW+tdc1Rs/vZGpS6cydelUCqoLDtlXb++c\ndwmf/+F5fmlSX+e40dCnj/Hz7A9T2328BkcDX6Z/efDx/sr9/G3xVJ7+5DMmPf0UL3/9Pi8t3MW5\nt3/E+KcfIqM0o9nj1NhqKGic23jHy8tbPGd7+3hJiWJQz/at6XpAcrc4CCmhoKD1tmBcqPryS7jr\n3bcAyCzLpKxOhmIf7qGVDzX7fmENMGb83fjpjSzZuYTVGatbTGx/zf+V6Z9Ph/9n77zDmyrfBnyf\njDZN996bllIoe++9UVyouFFBxYUTBwou/NyKIiBuWSrwU/beu4yWQhkFSuneeyXN+f5427Shg6YF\nBO19XWiTvGcl57zvsx8gMjmSKaumEJUaxfG04wCcSD/Bk6ufbNacuDthN9u2CaNNYKCEUgkff3tj\npB9cTn5ZPhnp4O9rbpApKBVK7KzVnE1LuirnEhcHfoZBSJViSisfR9Lzb641ooUbm8be5b8CoUA0\n8BiwDeEtHi/L8i3NPYnKvOWvgZFAOHCvJEltLhszGtFHOQSYDHxb3/4+3vMxL254EV2Fjrjs8yz8\nDv74HX5ckk12buMUy6zirCZ5TQyyoU6vUnPfhSFDAAAgAElEQVSRZZknfn+LPh9MJbeoaZbv+ibx\nyORI7vx5Ch1nTCE9u7Q5p2k2jV3cqwwdv0T9YvRqlenL0Bv0pBWm8fm+zxt9zN+if2PjBvjpq/rL\nicqyTEJGDr6ezSu8VYWNhQ2SVS6H4xKYtX2WSZ4oCMEvr1RozZ/v+5z5kfOvynHNYWnkBpAVRoH2\ncvwd/LF3KeRk7I3rESvT6ZGLnAkKAi9bL0IdIog7b2pNlmWZ30/83ugQT0uViBrYfH4zACX6En6J\n+oWFRxZiMMD3P8Bjv77H2jWwZrXw3gKEtYHycowL+KFKPbpYV8zUNVONecXlOuFVjk49wZLjS6rv\n74oy1q4TYdkysH0brFkj9lFV4Cihhve+pEZ68ILDC5iyagqASaTMD0d/YOqaqUbl+PI5Ydf+ImNY\n9/G045zLPgfAvMh5xvkwOi3aJCf6cqryrisMFcbzzCrOqjN/+fsj3zNj6wx2xO9g5vaZRCZHsjJ2\nJRfiwduiDecvQH7J9Z2TmkNKQYrx70uJcNucGcbUg8LyQp5d9+x1CS2WZfmqRUhll2Qza/usej8/\nmnKU9ZGnSEqCO26x4fHJ8PxtfRk+HIYNg9JSmLnhM7OOmVyQzPKTyzmacpTC8kJeWj2T77+H3bvg\nRAysWA7x8WLs4UjoNu3DOvczbf2LIEP37pBwTlvv8QyygXmR8yjRN76FUkZZAj7uTcsxdtA4YOdc\nZLyGhpBlmTc2vkN8POzbC6lZxczeNZtXN1X7DwrKCigqLyIp/+ooHzcbb2x5g7mH5pJZnEleWZ5J\nmpSuQkdesjsLFsCy32HKp2t48aelPLriSXbE7yAqNcpkHjyXfY7Fx5eQX1hBRlEGz//6HTt3wcgZ\ncxnzztd8s+dnvov8kb//hpQM8128U1ZN4eHlU3j+x19JT4PAIFj/+pv07AVvbn6LoGenEHMui0t5\nN05oVlx2HPHxcH/fQU3a3tZeR3Tm4QbHFJQVEJ8b32DLQ1mWSUuDsZ26Gd/zcFWDquymaIfZws1B\nYxMGAqsUYEmSFgIpgL8sy1erEV93IE6W5fjKYywFbgVqunpuQbSHQpblA5IkOUiS5C7Lci0T2/Yd\noFLCysC/OHNBnOJ998P/VsIby37j2ykPA+JBVEgKSvWlOGudRQ/X0lxctC68s+MdbC1teW+w8DKn\nF6WjkBSUV5TjZevF7yd+J9gxmC5eXUyOvT5uPX+d+otHOz9Kd+/utS70TNYZcktzmXfgexRKUChg\nQtu7GBw42MQzVZPE/ESyS7L5X2WaY8dXXyD+a1PFad+lfYS7hmOvsUeWZX44+gMPdXwIlUL8xCW6\nEp5f/zzzx9VWuGb+/Z1R4I54+TnSvr8+SllReRGvbnqVGQNm4GPnU+84XYWOQ0mHkAEJmLZ+GkqF\nkgpDBYGOgQzwH8CpzFOUV5RToivhZMZJghyDcLdxr7UvvUHPjgu7hKVem8UHuz7g9X6vm4wxyAYe\n+9+TnE+FV/r4XpVrtVJZYe9cxldH38fTUyw0Nc/vnR3vEOIcwgu9XgAgr6yJcbHN4LetB3HT+tZb\nXEOr1mJnB9EXE4CAZh9PlmWjgqZWqpu9P4DY83kgK1BX7s7XR8H6naZThN6gZ8v5LYxqNQpbS9sr\n7vNSWiG//AI8+AcAuy7uwlHjyAUuEHkYKvSw8TJn1NCh4OsHp2Lhttth506hIIAI469JlVd57trt\naL0hJxcWfA9lD28h8RKkpojQbAD3yltmy/kt/H36b9avE68fegh+/hmKi2W0WonDyUIIySrO4vUt\nr3Nbm9sYEjjE2EKnWFeMnaUdZRVl7K0RrRwZCeFtQWMJcw/NBeD9Ie8DQkHKKM7gm4PfoJAUDAoc\nxI74HbR1a0tUahQPdHiAFbEryC4sorVTWxxtLTiacpT3Br/Hm1vfpL17e6Z2n2o81on0Exw8BNbW\nsISlJCZCbi4kJ8PFeMiK1XPkEqx3hin3XfFnuiGYuX0mCy7L0PjIdzePjg8luySbigoRUu9r74uD\npvnRKHVxLvscH+0Rhf7mj5tPdkk2KQUptHVr2+B2eaV5WKosySzOJDE/kW5e3VBICpNQ/7TCNNKL\n0olwjzC+9+XeeWzcCH5+sOzRj4zr2NjQsUzfPB2AWV+fZnz743T0jOBKlOnLjC3O5kXOA+DvVeKz\nAQPBywuWLIYhQyA4GNZvgISLEH9Jh7+PCqnSEqWr0HEuDhRKGB46iO+21a4pkV2SzexdsxkePByd\nHp5fP4072tzOiFYj6jw3vUGPUlJSqi8lPx9Cm+gxdrJyQm2fTVwc9OghzrWuOfBE+gm+OvCVmH8A\njRWMmTON4GBw07qz7cI2BgUO4qWNLxm3mT9uvjCkr36CeWPnGb+PfyuyLJOQlcnBE5mUlcLUpNn4\neIvc1g+GfMDTa58mutJekJcr/qWmwNEj8Oefi1EqhQGnX1hbdp46QVQUpKVBQT6cPfMmBw+aHu/p\nD/fi4Ai5ObBmSy6P31u9jpfoSjiQdIA2Lm1w1joTlx1HmEsYMekx5Jbm4mPnw4EDEBUlxvv6wg/P\n30+Iuzcz7ridn/1WsGkTjPz4dRyd4PUhz3DvkDpaRFxHSnQl/LpnE6RHMG6M+TnGAFZaOF/ScORW\nzXt49tDZOFk51Rrz9+m/yciE8XcEGd9z0jqgsE8mIQGCgmptYiS3NJcVsSuY1GlSo887szgTB42D\nUY5u4b9BY39toy1GluUKSZKSrqJSDOAN1DSPJQI9GjHGB6ilGJ85Lf7/4KxNlJWCtzf8fNdcwg48\nxbzV+3i8/y18fPQ1JAksLYQg+uGt01h45HvOJebz58PfUqIvpURfytNrnzaxYFmqLPlq1FesPrGF\n3LwtjOzYgdEho/kl6hfuaXcP+xP3czYOZsR/z4ZnTBVjWZZ5ZsmnbN4MNZ0G3/EHwcF/EPdFbYV0\n2vppHD9dzIXK8Mw77oDly4XyVqovpaCsgMziTKbM+wmdDh4bH8pzPZ9jz8WDHEg6yPyx84jLjuOH\noz9yMQEyi7Io0RfjaeuJSqESSmcktAm2wdO/kK1br/BLIaz5n+79lE9HfHrlwQ2QUZxBeTkk56dg\nb2lfS0mRZZmLeReZvWs2Oj38+ANotTBmLOj1FVhYwJGcC3jQiQULwCA/w61h41h1WkhRn4/8HK3a\n1EuwLOYPFi6sfGGZR3xuHroKHelF6ayP20DkpWim9nqMHyvz5G4dad+sa6xCq9ZSkA+rVkGfvnBE\nm0onz2K0ai0pBSkUFRs4XpBEVGAUFxMgIz2PnaE7ySvNY9Xp1Xw1+ks0qqvjva6LOfu+JToafnt4\naoPjfO0CuHA+kyspxoXlhVirrckozuBoylFaObWirKKM6LRoIpMjyS0uoLAQcvMAGX5+4P9wb0L+\n0uUkpuhwdbIwvq5wjSLdOYqC0j5YWVigUqiM7Y9OZZ6iq1fXBgXH+Nx4zpwrp7QUMrMgIx1S0zYy\numNnoP6c8aoFevJkGBgwkMTE7SQnw5IlcNttRWg0wgtcUoKxKEnkuXP094aTl0Ql7dRK52NNh2lR\nEZyMBU/VeWNYfrfuGAvETV/6M/5hWZSVCwXz9S2vIwMrYleaFBDbdG4THT06svfSXuN+7pogImt+\n+VkI4MOHg7VWeGPSM+DNtZ+Qlg4O9lBSYqC0fAsF+VBQHMWqvyE941dAGCAVihPcey+cPgOvy29S\nVgaRl6JZoFzAgx0eRKVQ8e7Gr4zht3t21/4Os1UiZn9zVCxT7mtCs9hGkF6UjqPGkeSCZPwdqht0\nFuuKSSlIwdrCGg8bD3bE76CNaxvcrIUiVKovRaPSUFheyDcHv+HxLo+z+sxqYk+Z7t8/AP488yvx\nW8Hd2oPvv4fsnK8ZGN6WZ3s8e9WvR5Zlfji4jAULhNG1v/cKdiZtIDERhrZvx93t78DL1ov9ifvZ\neG4jHjYeTO4yGYBXNr0CiOiWwvJC5u77kef7PEG5DtRqkfP+xpa3MBjAw84FtUJFL99erKpUWre9\n8X8oFUrjuThaOfL5yM+RmcZ3C6DXc1+Tv+TrBo1gJboSdl7cicEAqWmQkCCescIC+OXNWxjRrht5\npXnY2nzCh0M/xM7Sjjmuc/jk51j6vPc0XbrC/41/np0Xd3I45QgnT8KzHWYQHhBLWtGpWsebvvk1\n4uJg16E/ObAf2neAzMwVWKmtcLN2w8vWC0ulJZYqS1IKUnh7+0xCHcO5I3w8eRk2dGyvrOMqroyt\nhS12tnAhPZ2DSfHMO/A9c8Z+hrWFaZOP3NJcDh8BWYZV7z/AE3N/5chhOHIYJCmNzNKlrDi1kpRU\n2LIFiosARKTIxQR48a8PeH/MC2hUGiRJIr0oHWu1da3jVCHLcoPz4cXci/jY+Zj8zvXR0L6udBxz\nWH1mNZGH4NRlP6+tbT4ZBU+TkiKxf5/wCIeFCQNlfDxEtIfj0WLsn3/C/1QnankdDx6E1q3B1g76\ndLUjpzifX34WSjHA/rOnGZ2vR6vW4qBxYOqqF9m4sQIbG/D0gsxMGN2xK0mGSDIzhawZFQWDBkGn\nYD+e7j+RQMdAAEa0GsGIViN4Uv06a7dnERMD95+cQ0jIM+xM2mg0ml9vFhz+jsXrz+MZ5ENTf7LR\nrcaw87va90yVcTwmPQaAjExYvw5OnX6NsNbQ1asrj3d53Dh+47nNlJdB167VJ+Jm7Ya1QxFnz9at\nGBeWF7Lu7DrWnd5M7Cno7zeAczlx7Ly4ExsLG25pfQuxmbHc2vpWKuQKcktz8bDxIDotmi/3fcMD\nHSYyMHAAIIx2BeUFFJYXMnvXbD4Z/gm2lrYUlRcZZU1JktBV6DDIBmO0WQs3F41VjNtLklQzPtiq\nxmtZlmUzO5vVorGJGpc/lvVuFxwM586BUgnzn3wEpULJoIHCEth35msmYYcAf/3vczRWUFoCnc89\nSU4OlUWGdLh7CCujUgkqVRlv9Etj5f/EYr3q7yjef9yJL5Yn8VnFpyY5pMOZglZ2xaDJ4EI8aDQQ\nWRlO6esLFQYx6TrYw8qVcOKUjrZhpkJD7LlitmwW4TaTxnTktdHjWL78XV798xsOX4qhsAjKyqon\n+JdizzDLdqrRC9VKWs53WzaRmgqFhdDh+OuUloK9vfA+paZCehrsfe1T1mZ+zdatx4m9kEubwPqV\nlNnLV1PmVMji44uZGDGx3nFXolhXzE8/wZGjC+nYEd4Z+jr+Dv7klORwKj6PR36YjYODWMxyKqPa\ni4uF8F6TPV4rAFj4HRTdu4qSUiGcX0yYxtqnvjV6MGRZ5kSMqTt02zaIa5/PI7+9w4HKukiXUucA\nsP+rZ3B0bPLlmSBJkjGkcs9uOH9uI9submTuhFnM3D6T7Tvg0vkK1DZzOXBALLwDjlRXUv1u4XNE\nRMDjnSfzzB1d6jlK05nz5zFsbOG+Oxq+YD9XZ7YV1d+QMKckl5d//IN1UZGUlYOFBaQkC8XNIIs2\nUPl1OMPHpL3Nr88+QRvXNrU/bATxyQXsPhvD+6sW4WjX0fi+p6MdkM+E76fh5wd3t7ubMJcwUlJh\n9oaFuLoubNCrMnvXbOIqz3fF8ur3PdyPIAN6vaiOebRSwdNohOD17uB3mbF1BgCdPDvh4XiEgwfy\nAcjKFl7ShATYX6OWzqlTYt6qUrY3VHqhq3KIQXx3u3dBfHwMEZXON28v8X8vb9h6dh99XOHnn8R7\no0bDurXi77vvAbUKJAWsit1ozOG0sICOncDRATw8hUJeWgJ/V3aeGjNWhIhfiaqIFjt7cZ7HokTY\na2R1KjbRnQ8Tkx5Dd+/uJp7qusiqTLOP0i8jrbBtnREgTWXKqimcjQPZIJS+pGSYNfxlFp74FLWF\nAT8fFeV6PRfiYfNz81l8fLFxWycrJ7JLsjl9Rngv9+2DVhanWXt2D7t2Qni4CKMuyIdWTq3YciQO\nSw1ctBMJ4lHHwIbM2qZfM5FlmT2X9tDLpxfncs6xKHoRqYWpRg+XwQAPztqAxkooTGvXxjC/dQxW\nWqE0+/lC5OEkNsZMYcn9X5OcIu45XY0w1EWL5hmNuAcPPGX0dEFVDQTxo5+f8y2BXrVDTbRqLePD\nbiVx9F+sWwvf/3WaJ26v3wM2Y9sMsosKjIbJKiIi4IEeYwAhCNeMfHq+5/Osj5zChg2Q/Des+vsL\ngoLhvMgC4OFnvME9G2y3cuwYdKyeHvjrL7H+VREdJf6tXLEIe3uxZoa3ha/uf4b3N85h82awtj7J\nsvCToHdt0EPVEJIkYWMD88/OYPNS2LEdDh95gTuG+vLWwOqIknJ9BYcj4ZYBAYxt35eRo37l+0rD\nrixXRZKY5q0fihSF/5ISYQMJ7Ip+nsBACHJoRQ5x+Nr78lS3p0w8cqtOr+LHPavRV8Ckts9grbam\na1tnPlyyi9jMk+AUh65c1DgoKREOBXsHMf9ZWIBc5EqJlIFCIZ6n4iLxTIWHi/FqFYQ4hJNTkk9c\nWiIaKxjWw5thof0YFNi08Nwq9ifuJzcPo/xWRUFB1TwoxMQhQ+HJYcNJK0ojKjWKmQNn8ta2mcgG\n0OngyBHw8AAk2LwJvH2gVTBMHjEAWZa5p909AOh0TwFibvvh0CIu/iCMkDKiC0FFpXJ9utJBE3M8\n0uR8/QNg03PzUdZjW/js1hm8PCSFnJIcuk5ZQLepc9Bo4M4vdPh5mxdZlV6UzkM/vMPpszq8vEBb\n4Y3OKglbWyhPC+LzSffSxsuv3u0PnLrID6tPkJ4Gm2Y2I2zHIQFd4HFKS8egUJejN+jR6WQiXnqB\nYcNg7z4RXVXFzh3i3y+aSN5yiGT19NfpEuyPXUkEirPeJnKZvaU9Dm7FtdISlp/4H5+vXoeuHBOv\nf6fjIpqmsBAgk9cRqUO2tpsIDBLrYEbl9HbyBOwNW8yOmW2QkPj24ALW7EngwgVhJN+69SW6BYeQ\nxVkunAelStxLFhYQ5OLN6pffavp31sI/RqMUY1mWm2YWbTxJQM2YVV+ER7ihMT6V79VCdT4Sbycb\n7KwLGTN8DGM69ATgpT4vsnvPp8SeBGsbKCqE0NbQoT389Tf4+ICDg6kgB5B2WevWNlPforCGmeCN\n70SRGG2lc9LFFTIzYNNGgNpKxC/v9WN48DAKywvxtfdFQqLD6acZ+dXTXJo7n2JdMUn5SXy89xM2\nrIfnBj7Mh891QqPSIMvg6gaf/BJjss9ZjwzidPk24s6aTgKvzt9kMi45CZAgOwujFzq8rRDI7/G4\nm3dcj3P7t6/Sv58IZ1FIChYfX8yYkDG4WruSVZTD18tFmGZ0zx3NUozzisSCXiWMlJV+QP/WHdh8\nPIqVNbrjHNhfzw6qrqlGq9pNm8V3D7BhPZwak014gAsAr215nfWxpnnjcWch/GnTUOo1qyHUz5Ee\ngVc3hGnESNi9W9x3KSnCGHLq1NskJlaG06pK+N//qkNrQYTj+vnBhQvC+PFs9AJuGfQ2/k5eV+28\nfj+2irNn4MK3X15xbCtPZxam1l8g5O+je/l+nRAE3NyFhxPAz18oxdFR4OIiDEOayvS8o0fh8LFS\npi9awl/Pv9Oka7jtq5kcOyEE+u7dqqWj29rcxncOP7N1K9x5p2hNZJBh1d/icysr+LC/Hkf7+gWO\nojpa+xYWweJKu0VNQbtNG9DphfBupbaiRFdCmEsYjg7VU2hdSmaPnuI+X7MGguqp89+/vwjJBlAq\nhOLo5g6vj3yMhUcW4u8vlOj2NaJVq5RiqA7HruKxx6C0TAgIfpWy0ehRsHtPddRNfed7OTa2GOfE\nnp792Ji3ixMxtccdOQKZWWXsdtrFpUvw5pNhnMk6RcwJcHaCXbuqx1Y9B2fPwunkZNxDr45iLMsy\np88IZaQmd5342Ph3+w56oiuVwPvdnmTz1up1IDg4m4sJoK+RCjdz5U/Cs29QcdcwX47FX6CrPJUD\npaLd1L4aRoDz5+H89hDm3leIjYVNk6/jWOoxfjz8K79E/UpJidjv3srahEFBwhAVf0EoKSGhwlB8\nusbveqQy5S/xEtxa9DRHj1KrSnLNyKZqpRgsLKG8Uh/z8ITAgPrLlYwOGc1fp/7CzR1e+mMOE0d9\nhp1V3R7L5KwCllTbILC1E2vTnhkN15Dw8RXeXnc32LSpWinWWEGHDhLJBS64+GXz29ZIOnbsCoi0\np9xcce+Wl1GrInCVkft4NAx6ZY7x/aIiISO0D7NusgcNxDp+/Lj4/kHMjelpl3igQzyBjgEAxCfo\nkRL689dLQimZN+4btmyZSnxlrTGVuvo+vPMusZ4dFUV78fMXIeaRh6pkmjj69IU1Fy6xdN1rxMwW\nIdeHkg/x3h+rjQa4VX+La3VxER7Py6mSb0ypfsPWThiFoNrooFDCXk6a3E+Rh5KYzVLOze9EkFfT\no4ViL2aSmgIP3+WO2jGN7ypTGZxdxBxSXgb9+kNwENze5nYTI+h3t1QbWJJGJOGidSEtt4BuUW8w\n5Y5QXhzwZK2os8X3im0m/PIU0dEVbNliej4bpr/LkrQZVKSGc2f4HXx24P84c74cWxsY1i2QSQOG\n16sUA1iprQhyDAJHEQ106KAwtn7+03k+f6O1Wd/NAz/OYGNlDbu8fMjOSsLGVjzXxcXnCT/wPl27\ninVEq4VXBk9h0+k9nE1OJzkvnd27xfzR268XQ7s00QoE+Dl6oFQd5+hROCh9y8mMk+TmCufTD5cZ\nwQYMgB07xN+lpcJ5c8tHH5A0fz4XLuoJ8zFtkWaltkKrhRNnCwARdVheUc6Xa9fVikTq3KV63oPq\n79fVVTiqoqNMx7u4CoO1x70zsNQIhbemYT8uDuLiztZ5zXne/818/2vN9u3b2b59+zU9xo0SOB8J\nhEiSFAAkIypd33vZmL+Bp4GlkiT1BHLryi8GcAm/kx0/126BEuocyuxHxrDq1BrauIVyJusMj3V+\nDG87b94amY2/vT/r4tbxtdUWdlUKoA8+BLpyOHAQ3FyFFfRSghCohw8XCva+vWJi+XHy8/Sa9gVu\nrsLSeCgS7r9PbOPqChUVEOLqzwMd7gfAnWpBr2sX+PVX4TXeXfgrfx06YhRqX3u0nTGMVpJg1/+9\nwKSFn1FcDN0qaxC8Ne4e9IY7KdGVMH3zaxQW68jJFQpAWBsRTv7QwL6sit7Ngrv+jxJdiTF/69W+\nooiHq7Ur4W1g/36Ro73VPZbI3HWs35nBl6VRaDSmwuCB/WLS8mhaK0e+3DMPhVJ4vC5dgmXL4Eyn\nKKP3rSbtO0CrVuDoKBZ+gwGOHasW0CY9KvISt2ypFqaOHYWJ37/B/rdFGPLOQ9lEHRPesW7dMC6g\nVcLFhAmQnS0UtahP6y7m0hz8/SApAGJqKAyxNaykERFCUAKRP/fjIzPwsHFHrVSTWZzJqtOrmfTW\nPga9+jXnv/ugzmP8deov2ri24Y01n/L2kFcI9wqkwlBBib4EO8u6Azvmb1+N1hoCfK4cqt02wIMK\nZQqyTJ1C4eJDa7CxgRNzZ+Jm60hOSQ4VcgVOVk7oDXoWRS3l8a6TUEpKdifsppt3NyoMFXg/+gI7\nDje9Iqets1CKO3eBr5++1fh+D+8edO/2M5s2weJKgbuq/yEIb8byNbk8NtG11j5lWeZsnLjPq+4z\ntVpYhBdXO/Np1w46dxaeWKVCPEcAbV3bGsO2HewrvyyJOuNcWrWqNgCdP1ftua1i9Bjw8RaKsUIp\nlPWMDOGx9LARD6CFWswxS5Zg/C6ONFDv5OgxUbhIaw2uDtZAESoVDBwAQYHiPo1oX61cj79NzIEg\nLOouzsJb6uMr5peVK4XH/Im7g9Ht3MW2baKftIeDI3OeHc29HywiN1cI6wmV4eMzhj/N7N0f4OCQ\nTGkpZGVhUvXcw9GO1Jx8/v5bov9LXBUKywvZvVsYRTWa2sIQmL63aLFpvPy5c7XHVz3T79xzN68M\n7EGFXIFWreWFDdA1p7axFb/dvPDHBRbc13SPQkp+ei2hsorX+rzFIat3SEoWwtxtnfuxO2EX8fGi\n2JuDveizHdEekpJgXWWu+vev3MY9Pfvz3LpptHIK5lz2OQwGiDkh7vv2EWJ/VVgoNLzQe9oVz3X+\nuPlcSpzCurWweEUeT9xXt2Kce8kLJ+dkBg8SCqu3gysZRRm1lJPLmTfuGwpHFHIk5QiBgcvQ6YRX\nPMBJ2NItlBa4u8PJ+GpN77fDKykvgw2zH2PJqYXk5YG+Qhho7DX2xJzNw9pGXPfZs8J7NHGimLML\nCuDYZ9OveN0N4VtH+YrUVAh6cDYvPxLOR7c/x4kLWSbrq0qhYuPbLxn7jldRUQHP936GOY5zKCgU\nrWwWTXmDh75/n7Q0iK18pqoUhaQkGDFnCs4uYp2MjYV2EWJujDomKutbWoqcbqVC7H/O/c+iVilx\ntnI2holuPr8FP3tf7CztcNG6cCL9BBHuERSUFZBamEqEewSF5YUUlRcZ64hcyL3AL1G/sjcqnW1b\nYfueYoLuappiXKYvI67yeXx99MOcyIymaOI6rKzARmPFuNBx/HLkd57o8Qg9fLo3GL7tbecNgJ+L\nJYkLGg75B/B1t+KBBws5dFAoT+8/344OvkEMD3VjONUK9y0D5zSwl4aZMCSETh3PcigSvtj/GeXf\nDOWbqXddcbv0onSeWDaDnTvhwY4P8uUbbVEpVCTlJxHiHEJifiLphRk8Pm8BkTUc2n/+Ic7b0lJ4\nP93dRcTeF+OHN/kaAIYFDcPJcRMb9iaTEnqSklIRraG1FmuESgVjxojox2d7T2ZB6+pCDZcSxRok\ny3Am6zTt2vSvtX8XWzvOnEkE2pCQl8DMre+zayf06QOBgfDLhHlklWTxxpY36NJZyC5VdYAMsgEJ\nid0Ju/npyG+AOA99BXTwC+DA6Xj++ktEI/j7w88v30OErx9bLmxBKSk5mHSQvHxo5e7Ji32e49lV\n01EqYP74r5r1nbVQNwMHDmTgwIHG17Nm1V8YsqncEIqxLMt6SZKeBjYASuB7WZZjJUmaUvn5fFmW\n10qSNFqSpDigCHikvv1J1G+OuzXsFsmChs0AACAASURBVG4Nq11I28tWeOAmtJ1AgH0g9yUvpG8/\neLX/NI6kHCHc5zy9fXuzLGYZLloXXu37KhISNhY2xA6JxcPGAycrJybcDQP8BzAseChnss7Q168v\nIHIVHTWO9SonM4a8xJ49n9Dvg6dpFwG7dkJAIEwc3hp3B9Pc29Yurfn72Q+wtrCu9CILSVulUGFr\nacsnwz8mtzSX/LJ8OgYvJtQlBG9bbwYFDuL+9vcjSRIOGgdmDap9Q7UOVbBzp4GYGLgr5hej1bjK\nSmxjC917iIV361aIPlmGh0fT8igcyyOwMxQyatQFkpKFZ+roUejXyZOgDinGsE+A0SGjWHdWSG9d\nuwrdopNI80QhwcLx8/l63wK2bDnM433uxLr1PooKk4g6Bnd8+S7v33cXZ88KpeKRAUNoH+zGcucl\nkNqJV18pobhY5qVBkzmcfJiCUQVorkE677DgYcTEVHvw774HbKxhx05h6X9rzBSeTJlPZiZM7vwk\nPnbexoXcRevCQx0fZMXYfaxenUVZWXVeaRWl+lIWR67l6JG1nD0Lf/7xEWFhwoNpoYaoD+aiVpk+\nG+vj1nPsKDzRunGTi5ujFVgUkp8vwvEvJzHZQB9exc9R5IR62prmhj7ZfbLx737+/Yx/Pzd2GJ9+\n0/SCY9nZ0K6VI3venGmSi61UKAkIFEpQlRe0yvBy70TRKmN59Fq6Du5AR4+OJvvUG/Rsq8y5t7QQ\ninH/AcLrlnhJeHaHDIH3K4tL+dj5ML3vdGNBsZq5UeVSHl27CSPS6lXg5CTOuYp23oGMHXeB1ZX5\nmt27izDr9HThWfLxhpd6v8SCBUIg1uuFt9fXTgj9INIy8guE4cjaGrp0EakjSYnw6GMixG/zFiEo\nRB2DM2fEsYqLIMzTn1T9SVq7tOZ05mn8KiMV9JUeHqUSxnTshrOVMwMDBjJ983Re6fMKH0kfMaLV\nCMaHjWdI0DIKygsY0b4D61MgJERs28s3DF9nZyZMqLYJfLdACEQWKjWDAwez7MQy2vm1RqOJoW1l\noMYfv4O7XyFWjpCTe/UqoS/cv4wKPRyf/S2Zpak8+MMslEohBJaVgp0dWKjV5ObrKCiAc3Hiu3pk\nkvguHRyFgUSpEPNTfh5s2y4MpW/e3c9E+B4XOpbcoqVkZwkDqb8/2NoKg8RPv2ewoInRickFyfyw\nT6SQKFXiflGphKf4zz/h9mGeHNotjI6PdX6Mbt7deKDD/cRmxKJVa4nNjMXZZSUDAvphpdIy67cN\n+AfApH4jAVgwzjS9YIpyCp08OzEoYBDOWmecrZwpKC+odz2ri37tAjh9Op6N+5N44r66I15S0wyM\nsH2Jge22Eeociq5CZ9K2qT5UChUOGgcGBw5mcOBgMosziU6Lxt9e5I27aF0IdWrDmbPCzV2qL+VE\njPAoDwzpRjf/cHYn7OZM1hlcrV25u+3dxHeNx1nrzMsbX8bHU02fPjpe6zud452P09mzc7NzZC0t\n4IEHhQJvYSFsZrl58Psy+PjHk4wIPkVmpkSIl2mBrxDnEGMoebFO1KmombM7ZDB09uyMn70ft/QK\nIytNy/snhRvZwlIY4VJTMXoSAf7v8ZHc0be98FTeCU+ueZIvRn5Bia6E1MLUelNc7gy/w+T1gACR\ni+lk5WTM2deqtVDDDhLqHMp7g98lvUc6/c9+xYGDMpOurOvVSXlFOYUFwggY4hJEiEsQEW4RxGbG\n0tevLw4aB8JcwoxKb2NpTDHIJ7o+QWxmLG09Yznf/zwvDph81XNKX+otrIGTmYIEzF2/uUHF+HzO\neRYfX8yJS5dYuVKk13zxYi8cNEKQau0iPM5+9n742fux563PWRy9lOX7D1BhELJUeIA749oOoqNH\nRxytrk4umb3GHnd3+Cl+Fu1tMdYlmHq/EzplNlO6TmF+5Hw0ltDBowP9/PsxOHAwZfoyZBmC//c1\nZWWQV1xKa7fanmsL23zidLuANiyL+ZMVy4XMuuvVeSYy1Nejv+ZU5imT4oFVqXb9/PsZZZKi8iKs\n1FYUlBXgabsSF9d9dPXuzBNdpxi3C3YSoV2Pdn7U5Fx+nXD9O4q0cHW5IRRjAFmW1wHrLntv/mWv\nn27MvtT62tXszKG1SyiDB4OtpS1hLmGEuYQZPxscOLjW+HDXcOPfEjAgoD9u1m7GQi0AAQ4BDR4z\n2CmYHj1FL9Iqb3Xc5/XnoThrnauPedkCbaW2wkpthaetJ+8MNlV4rrSYzxj4OkXF75GVLUKRkeCO\nO2HmqGfYnbCbcaHjeGfHO1iprbC1LmP/iWSGDw5scJ91IcsyMRnHaWU7lrcHPsis7bO4a4LwGG16\n9m0UColSfSkVhgoWHV/E+LDxRKdFk5SfhL3Gnhd6vUB5RTnHUo8Zv9uRrQcz6dHDPDswlFOZBlIH\nraCsHHYdyeQ952/JzIC774a7uvfD09aT229fQhcvBU90rfZ4VC3s14I7w+9k47lNhIQKoahKuFnq\nv4pZS1ZzW89O7M/24dMFiQxpF1Hrt1JICp4ecjvr1q0g8rCBPr1NwxeTC5L543chtPfrL0LMS8uE\nclVcBHYTn6Lkd9NJe/bKlWRnw/PvNS5M1VnrBNbpJCbWVoyLyotISzPweK/6c5bqo0srf8qUm83e\nDkSPxaxMeNLvfTSq2g9MT58eSAMO0KGD8P78b6UwOr0x5Fni4r7i8IW9vLZ8L5/c9Szedt7GasGL\nopcZ99F/gDDcjHN/Cnf3uSxeJBRNCeEhnjlwJgpJgVqprlOo6uTRiYpOwjQ/ebIIpV+1qjof97HO\nj3Eh5w0enwxUeuPHj8dYiR1Em6iwNqC1EiHJpSXwasfPcLexNhZM6tYVunUV7WByS3MZOlTk5auV\nCp7t+SQWFt8AQtGrmSIyOKwrZ7K1RLhHcDqzOt5WpRQKIYhzrOKbMd+gUqhMcj3vjagO8pkzeg6y\nLKNUKI2Cx9sD3+Z05ulKA8R0Hu74EAB9/frSw6cHaoUag2zgqTVPVf4GuUgVVjg6FhF/Kb+hW6DR\nxGbEsnTXIVztHLFQK/BUedIrwo1hwcPwtPGksLyQP07+wXuD3+O7w99xJOUInh5w7xhfXu3zKn+c\n/IOBAQPRqrUsi1nGkZQj3NttJI6O63mk0yO1ntmqsWr1Dya/ZVAQ/LGw6aHhpzJPcfiISLUYNRLa\nubXDzdqNIl0RlhMP4OSoYFKnSbRyamWyVlQpOP4O/qyMXYm/gx/9/ftz5+zbTfZ/+XW8O/hdnKyc\nTKqzmqMUgzA6r9v3Eds3RgPdTD5LL0pnxtYZJGTB3d3sjAXBZFlmYMBAs44DQgi+fK0ut4slWRsL\n3MrGcxtJSoYJHcYCYG1hbSx+VEVVUaTLOzlUvd9cvhnzDbmluUhIOGudSStMEz1f7d5g4Xfw9G+f\no1SBi2Pt7hZV1Cz4U3Wu0WnRtHMT1qVpvabx3LrneFA8agwM7sn+xP3IsjB6BTgEcFubW4jwMK1Y\nPm+siCbTqDRXTTm6HDdrN9zdFGSm5SBqq5rPlgtbSEyE2f3mGt8Ldgo2Ki2A2UpxYwlxDiHEOYRb\nWt9Cmb7smhZamjf2W071OE3bR78gLa26O8Hl/LZvE58sukRBvohISJjbsJKmVWt5rMskxre5BXtL\n+6vWHaIufH1FZMrFePF6z8yP6d3FDr1Bj0qhoqtXVwrKC1ApVNzf/n7jdrmluUgWxRw7k0VpCQT4\nWtTa94igUcxaJqLGtkWfJi8PFs0cU2seUyvVJkpxfVQVp7PX2PNwx4e5K/yuegvWtfDvwyzFWJKk\nx4AdsizXHVR/g6BowGPcGKoW/w+Hmh9O29u3N+7W5gs8CknBvZ3HYmuzmpxcEerWUB7KtcLX3pdF\n987nfM55/s/v/7gz/E6GBQ8DMC620/tOR6VQcWDTUo5F199zriEWHV9EXh7YOafhZevF/HHzmbJq\nCi5OShQKMZlVef6qhKTpfUXomlqhNk54fvbVSliQYxDT+72Ev4M//g7+dPXqSmnp6/z6i6jkTbEr\ni+97xyioKySwsWg4RO9qUxWeeGf4ncb30ssv0L8fKJUSd3ceScp9C3F2qvvHH9FqBE7OK4iJy6VP\nb1MD0JmkNOQCD84uf4qU4ngMsoHOnp0pqyhjyp8vs3QpzFt6kfFjLXHVupJdks2u3fDiwCn4+jbO\n++GqdcXZo4iCgppivuBC7gWyUq0ZPNB8e1srHwf0FQb0euH5MofzOedJTbJg7JN1f2cTIyYyNGgo\n7+8UbYcmTxbPaVu3tvQL6s6hgwdZvx5cXL5Cq4WPhn2EvcaeFZG7jOP7eQ1nzeqNdAz24WSqiDxo\n19qadwaJNITLPeOX08u3F5HJ1TFrLi4i8qGgQCjGLlqRBy9V/ifAIYD43HjjN/z2wLcB6N9P5EIe\nOSLyr7p1EIv1J8M/4bfo39idIGIlu3h1oYtnFz7a8xGWFjB3zFxjWDdUt46ysBRe7G4+nRgQ2AeA\nH4/+SAePDmQWZxLiFML2+O21hIkrta+o8mLXxMvWyxiZ81LvFwl1DhXXLEnG8UpJyecjPye7JJuE\ne9+lT1Ao6w+dYd26UxgMA4xzQ1NJyU/n4AFY/fRM47HfHfyuyZhOniLWfkrXKby/830CHQONtRRq\n1lR4vMvjFJQVYK+xZ3zY+DqNjpIk0cOnBz18ehCTHkNifiK6Ch3WChf+WLil1vjGsvXCVuIvwNqX\n36VvDytjRX+9QU9rZ+EV6uHTcHWvGQNmGH+PK1HTyNtUgp2CeXLg7UzcuJ3SUkyicjad20RmpjCM\njh1SHVYrSdJVE9Y1muq89fziUjLS4YHH6lc6rzUqhcr43APG4nK9fXsS3WO/Mef3uT7mFVts797e\n5PWkTpOMrdce6vgQj3R65KpWhW4OXk4O7D10AmhaPY+1Z9eh08GYUf+AsFSDa119WCEpCHFuhY2N\nqCEzbpzp5/G58by1aTZbtoj8brUajnzyfqP3X/M+vFb4+sLQYaKw2chR0LuLMKxVrSU1I6xqYmdp\nh72jgbhLeWRmQmir2r91kI8NJfo0ZBkKk73ppbqdiV2uXo2YFqX4v4W5EqwfMF+SpEBEXvBOYJcs\ny8eu+pk1A6mefsCNxUptxdjQsSgl8yfbhyq9IE1hXOtxjGs9jvSi9KsiiDSHIMegOnseQ7XF3M2n\nmJ1b1gKhZu9/18Vd5OXCWJ8xxve+GvVVg0JQXcJ2TcTiEWJ87ax1ZmqvSeh0PxB3Frzt1Sa9ouu7\nvmvJwx0fpqCswMSi7ap1NRbhyS/Lx+YKc7CTlTPxyYVAtWJ8Iv0EH2/6CQdlF/yc3PFzqjbOWKos\nWTxxHmfjnuDJRR/w2hro0U2FQdIjG2D2s50bff5atRZJAecultGzp2m8+e64KCj0MFZLNgdrSwsk\nhWij0aqVedvujosCZTkdOtT9uUalwc/ej7cHvo2zlTOF5YVGL1qbMInwtqJw0W+/ifD06OhX+PTB\nh4iLg86aCXw5qg/xufEMHLiRtm2UTPWbCnzD410mNrpScpCjCP/q49eH2IxYnJycUKvjKC0VXj+A\nZ3o8Q1F5ER08OojCSkd/NG7vZetVnTJRY9Z2rcz5lSRJeC4qyjiUdIhBAYNwtXY19vuWJAlLlSXz\nx81Hb9ATf3EqJ2JEXheYPltzRs8xvs4vy8dF69LsyrGXU6UU14VWrUVCws4WQl2DyI8oZI3bUX5f\nn8Q9o+vvd94Ydh9LhYv9GTOicbkSL/d5uV4jgEJSYK8RYRONUTLaubUzGhcv5iYAQhF0dm5oq7o5\nnyaKHY3s52aS669SqOjj16dR+2iod/y1IsTHGYVNNkejy+jVvVqZiEk7yQoRGU7bsGujZEzqfjfL\nl6yiXGdg6cEtUODNkJ7/7DpbFw91fIh9idWK8e3jmxfY18GjA1+N+orTWaeN69+NoBQDDApvz9If\nUq48sB46OvaDtDxsml7D7qZBpVDh5AwHjhQxbly1kGCQDTy9bDZrVoPaAsaOhbGdel4XZdccZg+d\nTXZJNoUTCrG1sL3yBpUoJAUatZrk3EzKM31p1ar2vRvi7QJ2O0lPl7mQmcSEjlenzWYL/03MmnFl\nWX4LQJIkK2Ay8ArwBTTTRXuVkWieYqyQFIxrPe7KA68R/7RS3FhcA5PJkpL5Y206d402/5yTU6DL\nqOoJ/lpYXXv49GDJxB4cSz1GoMPVCYFrDpeH2APcEX4HY0KFhhLhHsHy2OV1bWrE1UHDzgOmoaVf\n7hCVl/uF1/0dSpLEI6M6YKgQxc02bBJ5sA/0HIPaDIeMJEnYWlpTUqav9dmqqJ1YeNRdlOtKKBVK\nbH0SyMyU61z4GmLV0b3YqpyuGGFR5R2reZ8NDR5M8qhENu5PYs9uUXTj4EH4KuBnYk/CpP75aFQa\nKgwVhIaCWiXR3r099hp7o7LbGKoE0gfaP4AkSWw6t4m47Dg0GlHoCqojMgB6+vSkp09Ppqyqzmmq\nEmYVCpHrH3jZ7WyvsefRTo8yNGioUSjysvUiKd+0OqZKoSLAHwL8Td+roqaSbGdpZ4wYuZ5Yqa34\ncOiH2GvsWX5yOT6+EHk8n3tGN2+/sRezaRfQ+MquVzLGNRW1UoWlQzYZGU1TjPPzwFkKaVZV5H+C\nzp6dcXGG8xd1RsU4sziTqLOiKNZPr97e0ObNItDFE9TFDPzkSSoqICCk+IZREGuikBS83u810tNn\no1BAd3MthXVgqbKs5Um+EbB0ygDf3ZSWPtCkuh6ZqVY4yjeHvNRcJEnCy9GRvbEXger0vQs5F1iz\nGqy0cGreTGN9jxsNJysnkxZh5qC11bH39BkwqOoMI3fRuqC1LeNwVBnpGTB8fB2V7VpooZGYG0o9\nA+gN2ADHgBeB3Q1u9A9g0cwc4xYax+1tb2V/27948c/PuWv0bLO21Rjc0OvS6dmjeUaMxnJ5YaUb\nCQulhVEAd7N2Y+6YuQ2ODw5S8POeP5HldkiSKMCyOzIPB0f4491b691uavenSC96m27dUpGBIJtw\npg+qXYjuSlhal3EmvhAxDVSTngGdFU2LmHDQOKBWQUJKMT0xL2wpOxsitCOuPLAOAhwCeGvAWyTl\nTyE8XBSaW7miurXRrIdENc6yClG0pyqk6qNhH5l1HI1Kw2cjPjMK4r19e+Nh48HXB79ucLvnez7P\n2WzTzBU/ez/uuTuBugJjJEkyqWcwrec0KuSKWuN6+vQkvyyfkxkn+WT4J7U+vxGoym28p9097Nm7\nlItJJVfYomGKdcXEZBzD36cJIQ1XGRsLGyxti0hPF1VfzSbPjzBDEysW/YMoJAVajZrjZwqomj8S\n8xNJrixM9kCfa2eEyS7Jxt5BdJGws4NApxvXqxTgEMCkvmNo59bOpJjgvw2DVIqkEFWyg+tpU9cQ\nWy5sxCX4nwuHv944eOawfs9SQLQ11Bv0TF8l1qLUnz7Hzur6poZdL2wUrkTn7cKyHsO7lcoKe49c\nHvn9OdGeq1/tMS200FjMjdG5HdABaxBh1HtlWS5reJPrj6IJIdAtmM/okNEsCPmLv05kX3nwZSQl\nG/AoGIuXS0vuhrlYuFwCG1FUy9apmHt+msbpUzB/0jTc7Rtue1FXJXJzsVE4U24wfexlWSY7C8Y1\nsfezjYUNjtZ2JCbXVuKuRE4OjPZte+WBDfDlqC8pryjnaMpRTp5YzOnT8OCD4OMm7s+ald+bSs08\nJWsLayLcI5g3dl6dimsVbVzbmFSE/Xr01xSWFzJ98/RGeXLry416qONDyLJMflm+MT/1RmVQ4CDa\n2p8n/ZL590ZNVsauJDsHbm31z3sTrFRWaDQQGyvTv7/5Xsvk3Cza+t+c65y7gz1nzol894u5F5l7\n6FuiouD+9vebpLpcbcoryunfTxS9y8+HESOaoIldR25pbb7R8mZjTOgYbKz3ExPTNMW4XAcedk0I\nubhJ6R7mzXrrJI4dg44dIbUwlZ07wdOLf61SDOBop+Z0DHiVDanzcztLO1q3hu3bxHeh/fd+FS1c\nB8xahWRZ7gQMBQ4Cw4AYSZJuOI8x8vXxQrYAb414BopdyTezaGx2pooIp243ZCjbjc6zPZ9Bo4HV\na/U8vnwa69fBhL7deOzWpriezMfZTktOnmnRtWJdMYWF0DXCvEq1NbGwgMJi85QfXYXo192lXdP6\nYFahUWmws7RDqVAyYIAouLXgtuo+hG3d2tZbHKQ5SJJklrKtVqqNHqSxoWObfFyFpECpUF6zirNX\nG2vHQuKym1fzMcgxiOTILozo4X/lwdcYlUKFkxPklGdeefBlyLJMXkkREa1uzsgoR69MVmZ8gE4n\n88aGD4x9qyc/em0LGLV2aY17jZ7Ab05o+vPTwtXB2coZB0fIK2xaEc/SfGu6u9atLP0bub/Dvbh7\nwPxl8QC8tOpd0tNhz9sf/7Mndo2xs9JSVgbe9h51fq5WqundwYXJk2HPh83rL95CC+aGUkcA/YD+\nQFcgEeE5vqEoL2i6cN6CebjbOWLhmMGxY9C/dt/1ejHIFYS1bjFgNIV2bu0IDoapa6fi7AztgtxY\n8vJjV97wqiFzKSsDqM59yyzOJCvNumlhoZVotDqOncoBGq+sbY/fTk42dGp/dSrXVimpr/Z91SQX\nWaPS0NWr61U5RnO5ll61G5Vci5MUOgM0sfEvkJiVDTotPXtetdNqMpIkgQy7ErcxnQlmbVuiL0FX\nDk62Vtfo7K4tfpXF5rrOeoLoqMo3JegdYF71ZXPxsvWis2dH2nc4xvlzYKtpcSv90ygVSiwsYMfZ\nSB6kl1nbGmQDRboi7GyvrUHlRiLEOYSOfq3YGbeeexYdZcMGCPS3INDr3y3z+riItAffwPoDVN8f\n0vgq3C200BDmSlizAVvgKyBcluWBVQW5biQCbtIQs5sRDxsPnJzgQFSOWdvl5hmw0vz3BPyrRe/e\nosdschKseKb54dHmEOjmDpJs8l5yfjoV+S6Eml+g3EiwqzfZOeZ5jBcd+xNZhvDwK49tDD28e/DJ\n8E/MKqx1vVEr1XjZejUrrPtmY0LY/eSerqfseCM5n1COlaXarGJz1xJ3RzscZfMLAuoNeqRyO/z9\nb85om8e7PE7XbhiVYk9PmPZIAErFtV+3e/j0oGcPmDjxymNbuD7Y26hRy+anVJXpy8jPtqizr+2/\nmVB/e05mH2XZUtGj/vTnX115o5ucAH8hK/YI+OfrQ7Tw78fcqtQ3ReyRWtWicF0vlAolDg5w/Ew+\n5nj6yinCStNiwGgqC26ZT1nZFLy1rYyLxvXkXGqayetFh/8HNvnYNcNwrbQsJ0MXD4RcaaiR7GR7\n7DP6mt37uD5E1e0bO+dWISmMfY3/K3i5akBrfthxTc6mpBLg+c+HUVfhLIVw/lKp2dudyjxFWm4+\nFjepPtDVqyudO32Hny883uteVp5dwptDp1x5w6tAZ8/OvN7v9X91QaubDTdFa85eMP85yCnNoaS8\n3Oz2fjc743qGMeePw9w1xp1Zd0xErb45DWTmkK+IJ7wtjBjeIjO2cO0xN5Q6FPgAaAtUrSyyLMs3\nlHtFpWxRjK8njo5wOH4/0HihUyeX4utxc4YC3ij8fNf178MMEOrjylpThzHnUzNxktrUvUEjKbFI\n4IJVAqJ8QeNIy9DTJ7DxfZhbuDnxdnKGCjU5OWK+aQplpRLOmsb1nb4euLpIJErmV9pOLkhGbQG+\n/3wNsSYze+hsFJICB40DI8MGXtdj+zvcOMaRFsDdTcHFhGKztyuvKKcs3a9J7c5uZoJdfXh8MswZ\n9cY1aXF5I3Jb2G1kFC3A0/UmtQa2cFNhrgb5IzAPUZl6IPAzsOgqn1OzuVreoxYah5MTnGdro8fL\nskxhAVhb/jcm9X8bVpZKsrJNQ55zciBcal4P0tvDb8GQal6oVE5hEe1buTTruC3c+KiVKqxtDZSa\n71gykphaipP9jbM4OFu5kHDJ0ITtnCk80a9Z0Rn/NE5WTjhomlcwr4V/Bw6WLiQlm/8cZBRlICkr\ncLo5a9A1mSDHID4d/sl/RikG6OLVhXlj52GvuXFbrLXw78FcxdhKluXNgCTL8kVZlmcCY67+aTWP\nAFfXf/oU/lN0CQg1S2A1yAYMFQpsbf/9IUD/RpwdlRRVVOeU6w160Us4wKtZ+/VxdqZMLkCvb9x4\nvUFPYSG0CvjvCAj/VZSSEr1FJllZTdtelmWSymJp0+rGaQ/n46UkpyTP7O3SCzMB+T/nKWvh34mr\ns5JShflpEjq9TGm6N7Y3dubLNeFGT/e5FrR0MGnhetEoxViSpHWSJAUCpZIkKYE4SZKeliTpduDG\nkTQqsVbb/NOn8J/i9ojRkO9NSSOjAssrykEy/Ocsvf8W7GwsUKirtddiXTHF+ZZ06tA8b5yvszMq\nhYriRkbVpRamkp8PgebXL2rhJsNB44ClTbHZbeGqyC3Npawc/G1vnN61Tk5QpjO/TY2uXAHltrTI\niS38G3Cw0ZCdZ/5zkJSTiUYjoWlJF2+hhRauIo31GP8AbADWA1rgWaALcD/w0LU5taZTUd7iQbqe\nuNk6oHRMIiOjceOLdEXIOs1NWzzmv46LjT0G60TyKp1dOSU5lJZV4NU8hzFqpRq9dQIpKY0bX2Go\noDjNi1atWjSEfztatRZrLeQXm5+TC3A66zTZic4EBt4494qHgz1ocsgxr6A/mdkVLcWjWvjX4Odh\nSxGpZm+XkyNTmn/D+WVaaKGFm5xGKcayLP8BdEZ4h3cDdwMxwB6g9zU7uybSKril+Nb1xM7SDq3K\nmsTExo3XG/RkJNrfMG1TWjAPV2sXbK3VFBSI13qDnszzvvg3s6aNk5UTzo5qCgsbNz4lPwPZoMT9\nxqmn1MI1QpIk5DIbzseb186ripySHAoT/Ym4gbp9GGQDGv+YRs+bVZSWGXB2aqnO2sK/A39XZ6iw\nIDfXvO3S8nPw8/jvhRS30EIL1xZzNEgdUIyoRm0L2FT+u+FmJkt1i9BwPVEqlGitKzh1qnHjy/Rl\nWGkNeHpe2/Nq4dqgVqipUOcY+VtgkQAAIABJREFU8z3LK8pRq5TNrpJrpbJCsiwiMblxys+Z5HQo\ncqWlhtt/AycnBQbZ/CI9APlFOijwbnZUw9XEw8YDjQazFeP41FwkuWWNa+HfgVqpRGNdYXb9gKxc\nXUtrzhZaaOGq06ikQEmSRgKfAauATrIsm19b/zpioW6ZLK8nKoUKR9dSLl7S05hbKr8sH4POosVj\nfJNibWGN2rrQmO+ZnJeFrlxCq23eftVKNZZKS/ILdcCVBf/UrCKcNG7NO2gLNw1qlYKMzKYpxnHJ\nGWi17jdUXm6gYyA2NnDqXAmjaHzrOhnDTd2qqYUWamKQDf/P3p3HR1mei///3DPZSUISAiQBQhIQ\nBamItoALGnel4GndOVXsqVb89if2dPsKrVX8FatirajFHvWICq2iIC6homzGghsiIEuAsIQQEgjZ\nJ5kkk1nu7x8zCVlmkkkyW5Lr/Xrlxcwz9/M8V4Y788z13Bthw/dz9CiM6cYUAA2NduLCZKISIYRv\neZtB/gG4VWv9kD+SYqVUklJqg1IqXym1XinVYR0HpdQopdSnSql9Sqm9SqkHPR3PaJDEOJDCDGGE\nR0Bx3XGvyjfZbFiqhkhi3EdFhUURGxOOxeJ8XlnTQLRjuE/+PwfF2The7N1ELBsObyR6SPdnMxV9\nkwED1TU97EpdpUiMDq2lPqLCoogdBGXVXo4dcLHaNNEdL5FC9ElGg5HBCbDtm+7d9DptqiZ1eOgs\nvyaE6B+8/VS5TGut/RjHfGCD1nqxUuoh1/P57cpYgV9prXcppWKBb5VSG7TW+9sfTO6mB97IQZkc\nOFwOZHVZtrD8NECvWxhFcIQZwtAGK8ePa0BxqsoM2jdNceGGCCrNNXgzQqOu1sikqBt9cl4R+mIS\n6jBX1QLdX6fIVOtgZGro9bkfHJ7MsVM1gPdLDJaW2bE0ys1f0T+ck3wOCQmw37QNmOb1frUNFmIM\n/SsxliWJhPDMv2noGV59qvg5KQa4Ebjc9fgNIJd2ibHW+hQ4py7UWtcppfYDaUCHxFhaIgMvY3gi\nmxtLvSprtxuJMw4NqW6NwnsGZSAiAuqstUA8tXV2EsJ9s3Z4yuBkSk913XLg0A7qzHamjJSWs4Ei\nXo1k/5Huta42qzVbCTeG3rjc1ORYio92by1jg8FBVqYkxqL/iI2FL068TXcSY4ddMWZkvP+CCpJA\nffkXoi8J5E2jULm6DtdaN2dVpUCn88wqpTKAycDX7l6XxDjwhsYlUlvnXTdHU60dqyX0vqQK7yVG\nJVJT61zLuLy2mqREH/1/Kis1dU1dFqu31tNogZTk0GsFFP6RMjQcHdm9JLJZlfUUI0aE3p24pJjB\nFJZ273cqtx0jPEw+P0X/kZAA5sruJbmFNYU47PJ3IITwrYAlxq4xxHvc/LTpC+lqnfZ4y8zVjXo1\n8EuttdvmA5ntOPDShyVSY/FuvYXS6hpiB8kFrS9zYKegxLleU3mlDaPyTZc2FXeKg3ptl+UOVRyi\nqhIyMnxyWtEHDIkeyqHDth7tW1MVTpTufhdsfxufPozKRi8XgHepNNcyJEzGC4n+49qMH1JX5P3M\nW1prFDA2U1pBhBC+FbABGlrrazy9ppQqVUqlaK1PKaVSgdMeyoUD7wL/0Fq/7+l4Tz+9sGUJl+zs\nbLKzs3sTuvDC0KQwzI0Wr8parDaGDInwc0TCn4YnxkKls2XXru1kpfmmS3Ny9HAOlWZ2WS46PBpd\nfna3ZjEVfVvqcCPlqW9SXjuZ5LjutS7VGYpIGxblp8h6Lm14JLUqH4cDvJ0zUjnCiTR6P4u1EKFu\nXHoC9cY8r8vbtR1znZHUuBQ/RiWECDW5ubnk5ub69RyhMnPBh8DdwFOufzskvcrZwfxVIE9rvaSz\ngz3yyEKi5XtDQI1KToLwBhoa6PK9L6+0Y7QkByYw4ReDwuKprHJ2nS8oKyXZ7ptuqt8fdR4f13bd\nKmh32DHV2klM9MlpRR8wItXZOvTBvxq5547uJcY2O6QkhN54dEOkGYbkc+wYZHU9byEAdu1g1IhQ\nGQUlRO+VWg9DQgE2G4R58a20or6CJpud2Fj/xyaECB3tGzsfe+wxn58jVK6uTwLXKKXygStdz1FK\npSml/uUqcwlwJ3CFUmqn6+d6dweTMcaBFxEWhiG2nJKSrstWW8pJGBwqVU/0hEEpyqqdK7cppTk7\n3TfrSSbEh1HtRWJsspgwGDXJcn9lwDhVV0JmFmw/6MWHTCuNtkaqq8GoQ6+XymWjLyN+MOzN876L\neJPVTkS4fH6K/uOqrCtRCk6c8K58bVMtltMjZdicEMLnQuLqqrWu1FpfrbUep7W+Vmtd7dpeorX+\noevxVq21QWt9vtZ6suvnY3fH8+aOo/CtxOhE4gaFk5/fddkmu41hCV0vxyNCV1KSwhHmHOJfbjIT\nF+2bSbDiYo2Ejd3cZTlLEzRVDZMWgwGkwdZAXBzsMW/q1n5N9iYiiWPMmNCbfKvJ3sTgwVBa6916\n3FpramvBYAi930WInoqPjGfQICj3cll6m8OGuXoQwzudplX4y6RJk/juu++CHYYQfhESibHo+8IM\nYcSllXDoUNdli6pOEYEsYtyXJUUO5USxsyt1E3UkxAzyyXG1wYLNBk1dTEx9srqSmGij9A4ZQGac\nNYPBg6Hp+KRu7Wd32DFVh7XMOxFKhg0ahtEIe/O9W4aq3lqP0SiTzon+ZXDkYMLDobLSu/KHywrB\naJGhNEGyaNEizjrrrGCHIYRfSGIsfCIxKpHB8fBN4Z4uy9p1E0NjQ2+GWOG9wYkOGgyn0VpjrlNk\njPTNoP4rsy7HYEmmposVbGrrHNitMrP5QHLe8PO4IPlSjlee6tZ+NZYaLLqOJN/09vepmPAYxiSM\nA+XdUndN9ibqKxKJCL1e4UL0mEEZiIuDhsau17AHMNVqws1ZIXmzayCYNWsWMTExrF69OtihCOFz\nkhgLnwg3hjMoFgpMhzst59AOLLYmRgz1TQujCI7RQ4ZRUW6k3lqPpUmTmOCbjxKDMhAT48DSxQTn\nNbU2YsOkuWCgaYw5RE3Clm7tY7VbMdSNCtnWJaWNHDriXWLs0A4sjSokk3whekophd0O+w6bvCq/\nv+gUBqN3fzPCf+x2+T8Q/Y8kxsJnvpc4jbLizrtI2x12TDXhKC19YPuyoclGUHbqLPU0lCeT4qNV\nMwzKgNXuoLS083KVDZUMHSKTCQw0xoimTla5d8/cVE+dyUgITkoNwJBhVqot3vUhdWgHRoOR+O5N\nyi1EyEtIBLP7lTo7cNiMnJOa7ueIRGcqKysZMkR6/on+RxJj4TOj0sI5dbrzO4h2bSfMYGTs2AAF\nJfwi3GiEqGr2F1Zi1Y2MHOmb4xoNRuKGVrNlZ+eZsbnegdLSlXqg+eE519LYCLobybGp0YzCELLJ\nZHLMUK/HVpbUltAUViZj60W/ExYGh4srvCpbWmbHbpOvr4FUWVnJypUruf322wHYunUrl1xyCWvW\nrGHevHlBjk4I35FPFuEzI0cYMEUc6PRLq91hx1xnkLFBfZzWmpixO9i+wwY16T5bNzwmPIbkZHjv\n8D87LWc2ayIJ0UxH+M3EtLEY6kZ1OTlba+Z6jTaHbstGanIkpyu8+4U2HcnFZkNmYxf9zsiIc6k8\n6d1neoOtnpFpA+/GqFK++emJ7du3c91113H06FEAzGYz0dHRzJw5k/hQvesoRA9IYix8JiN5OAw5\nyOlOekPVNdXRaKsnKipwcQnfGxE/gqQkeOfLz4lJ92KNLi+FGcKIHQR1TfWdlrPZHYxIHXhfjAY6\ngzLg0A7qO68ebVRU2omOCt1u90OGKKpU53MzNBsxKJNwR7zcWBT9jh5cSJHjG6/KFpaVExUZun/T\n/qK1b3564tprr+Wtt97i1ltvdcXiPJDJZOLqq6/21a8oRNBJYix8ZlLKJAYZkjh2zHOZJnsT4Y0j\nfDYmVQRH+uB05yzkJ74lWfl22Ya4OKgu7/ybf1VdPeHh8vE10BiUgfAI7dV66c1O15WRNMS72W6D\n4Zy0kWBs8irZV45wwqsm+j8oIQIsPKaOo01felW2Xp123ogXAZWXl8fEiRMpKCggMzMTq9XKe++9\nxxVXXBHs0ITwGflmKXwmOiya6CGVFBZ6LmPXdmqqwmW5kT4u0hhJ8zKG41J8NMDYJToaKio6v61d\n3VgjY4wHIIUicUQZJSXe71NWBk01oTuN89DYRMLiKjnlxSpUNbUOGqpCdBYxIXohZhBEeNETQmtN\ntcnK8ITB/g9KtDFv3jzWr1/P888/T3V1Ne+++y4//elPgx2WED4libHwmZjwGOLiYPchzzPJVNRX\n0ORoYLjc7O3TlFJMn3A2t98Bf3voYp8ee3AC1Dc1dH5+bWTMCEkQBpr4yHiiY61s3POd1/vUWCsY\nMzp0x27ERcYRk1BPWVnXZc1mBynD5bIt+h+jERo6/9gHnCsS2GwwJEFmoAu0s88+myVLljBlyhRu\nuOEG7rjjDsJlJkDRz8gVVviMUorUuOF8u6e20zKG+jSfTdYkgufXF/2alT95ibPT0nx63NjocKxR\nJZ2Ohap2FBMVLt0OBpowQxiJCbCx6hVyDuZ4tU9ltY0oY+h+4CRGJRIRX4VrTptOVVU7GBQjl23R\n/1x7VjYOO3S1NK5d26mohFGpoXuzqz+z2WySDIt+Ta6wwqeik0vZdXqHx9ftDgcOq1GWGxEeTUhx\n9tGuq/NcxlQVjmqSmTAHGoMykJgIpyusvJe31qt9TE01RBlDdxrn2IhY4uKg0WrtsuzOiq3ouG70\nIxeij7g86xLC6kdhsXReztxkRtcnkZkZmLhEW2FhYdxyyy3BDkMIv5HEWPjU+RmZnKov8tjaV1Xt\nAG3AIDVPeHDdmGsxGKGqynMZY5jm7LMG3qykA12YIYyUVKiugg8+8G6fE3XHGDGii2aoIFJKER0e\nQV5R1wlvnc2EStsegKiECCyDMmCzO6j13OEMgEZbIw2maBmOJYTwC0lPhE9dPv57MHSfxyWb6hvt\nJCbIpEnCs5HxI4k2xHocc6m1xu6wERUh9WigUUoR52r8razourxDO7A2QUrYeP8G1kvxjKLBYuuy\nnNkMaU0yA6zof4zKSHSMg/LyzstV1TaCJZ7BMveWEMIPJDEWPnVh2mRiBsG337pvMi6tLcMQ0UVf\nKTGgGQ1G4gZrj13q6prqqDE5kyQx8IyIH8GMGZBq/F6XZZvsTdTWKs4eE9rjEQcnWTlU3HWmH+lI\nJNl2fgAiEiKwDMrAoKEVXXal/lfep0Sk7Uc+/oUQ/iCJsfCpIdFDSEyEPQXum4xrTUZs1bKIsfDM\noAxY7U0UFLh/3eqwYrAkMWpUYOMSoeGPl/2RqWkXY9QxHK06yu7S3R7LNlgbsFqMJIT4BObJgxL5\n9puuL8d2u2JMWmIAIhIisOIi42iyN3HsWOfldhcfJLzRtxM+CiFEM0mMhU9FhkUyaBDkle1z+3p1\nQw3JiTI2VHgWbggnYYgVi839ZETmJjMou8xsPkAppcgYPIYmYwUvfvMiS7ct9Vi2rqmO8pMxjPTt\nUts+N2pcFRVDup5MrKbKQJhRLtui/wk3hJOcFOZxGFazNHUB4yOuD0xQQogBJ+hXWKVUklJqg1Iq\nXym1Xinl8d6+UsqolNqplPJunQ4RFGclTKCyeIjb1xqamoiLlz5QwjOjwYhRGTlwxOz29QZbAxWn\noomJCXBgImQMi0/gdHEUtZbOZ+qxOqwYm4aEfO+CCttxiD3JF/n7MTeZqW6sdlvOoR0kJwf9si2E\nz4UZwjCE2aio9tyXurC6kILKImIiZKk+IYR/hMIVdj6wQWs9Dtjkeu7JL4E8oJMVTkWwRUcpau3u\nZ06qrdNE2qUroOhc4qBBNGqT29dqLbWE2xNlVtIBLDXNAcP2UlUNpZ20MJ2qqcJqsxMf4it7RRqd\nX/SveWQJf9r8FxZsXOC2XHWNJmFwKFy2hfAtpRRD4mIxNzV4LPPnLX+mpLqMUSNkvUchhH+EwhX2\nRuAN1+M3gB+5K6SUGgnMAP4XkCbHEJaeNJxDh93fu2i02DEaZDZh0bm48CHsP+h+iZ0GWwN2qxFp\nNBi4zNY6IqNg40b44H14N+9dTtaeZG7O3JYyhyoO8dL2l4kiMeTrytPXPk1sHNSb4Z8flPBhjqND\nmY8OfYTFUMXwYXL5E/2Tw+Fg3+HOe4FYLJCZJlNSCyH8IxQGew7XWpe6HpcCntqBngV+B4T4vX+R\nNgJKakrdvma21pGWKomx6NywobDzpIcxxg12HOYhhIXCp5cIikhjJBHhZ9a6/uTIeoYOGgo4u1u+\nuedNxiSNwWwGS13o97mPCovi1lshNxcKjgK2jgPoPzjwAQ4HJA6Wii/6p0EJ9eytXYTV/jfCjWda\nhQ+WH+RQ5SEA6ushcbB8hxBC+EdAWoxdY4j3uPm5sXU5rbXGTTdppdRM4LTWeidetBYvXLiw5Sc3\nN9dXv4bw0gVnpcKwvezb33FdzrJqMxHhodBRQYSyhCQbB08fcftaVY2VmGijLNcxgBmUgfAIWq4W\nRUVgb3Qmk18Xf82x6mMUVBVgs0F6evDi7I4hg+LPzJ4d1kC1m2HG1VUwPDE2oHEJEShR0XD0CHzy\nbT7gnGjRoR089/Vz5BzM4auvoaQEzsqQmReDadKkSXz33XddlluwYAHPPfdcy/ODBw9y/vnnEx8f\nz9/+9jd/hjgg9dX3d+rUqeTl5XlVNjc3t02O5w8BufWstb7G02tKqVKlVIrW+pRSKhVwN2LsYuBG\npdQMIAqIV0ot11rPcXdMf71ZwjsWRz3Jo6p4dvUX/O8fL2vzmnYYiQ2TblCic5aoIhzjimhsvIGo\ndkvQnqotIya2Y1dTMXAYlIHKVsv+frwODu95lytnQPpgZyacFpeGqeYo4Vb3EwGGmsXXLOaOw/8/\nOykBWxT5+TBlypnXza656EJ9IjEheurKSWexfv0higqiYAr8+pNfkxCVQFW1nUOH4Xihs9yF35Ob\nQ8G0aNEizjrrrE7LlJWVsWLFCo4cOXODe/HixVx11VXs2rXL3yG6lZGRwbJly7jyyivJyMjg5MmT\nlJSUMGTImWvE5MmT+e677zh27BjprruqBoOBw4cPk5WV1VJu4cKFHDlyhBUrVgT89/Ak2O9vT/32\nt7/lkUceYfXq1V2Wzc7OJjs7u+X5Y4895vN4QqHp7kPgbtfju4H32xfQWv9eaz1Ka50J3AFs9pQU\ni+BLH5zOuefCqgP/7PCa1W4nLUW6QYnOxUXGoAy4Xbqjtjqc+rJhgQ9KhAylFNOmOR/HDHL+W++o\nYuXbUGaq4VghFFWW0dAI6aP6xueNUoqp5ydw442QMrKRQ0fa9rgJK/s+GdaZIT9eWoie0jhISwNz\n3ZnuQNWN1eTnw7fbITYOsrMhdbgMJwimWbNmERMT02ki8/rrr/PDH/6QyMjIlm2FhYVMmDDBbXmb\nrWMPQ19TrbqZKaXIysrirbfeatm2Z88eGhoa2pTz5liB4M3709n764vj+8usWbP49NNPKS11PwQz\n0EIhMX4SuEYplQ9c6XqOUipNKfUvD/vIrNQhbMLQCYweZcBkAke7hr1TNZVoR9/4oiqCZ9GVi4iO\nhqMFHVuGm2x2xmRJHRrIwg3hLbOSN1/PGxvBVAMnS+2s/wQ2bT/OV1+CtSkULnPeGRY7hJQUiI4K\n40hJRZvXTlfXcf6YlCBFJoT/aa2JioKDh5wTL2rAagNLo/Pz/kQRXJY6I+BJiXDPbnc/QSbAxx9/\nzOWXX97y/MorryQ3N5cHHniA+Ph4Dh06REZGBosXL+a8884jLi4Oh8PB/v37yc7OJjExkYkTJ5KT\nc2Z11oyMDP7yl78wadIkYmNjuffeeyktLeWGG24gPj6ea665hmp3Y1A8uPPOO1m+fHnL8zfeeIM5\nc+bgHNXZuc7KPPnkk4wdO5b4+HjOPfdc3n+/bXvfU089xciRI4mPj+ecc85h8+bNbo/j7v0pKSnh\n5ptvZtiwYWRlZfHCCy8AHd/fw4cPeyzbk+M3l3/mmWeYNGkSCQkJ3HHHHVgsZ5ZXKyoq4qabbmLY\nsGEkJyczb948gC7jiIqK4sILL+STTz7p8n0PhKB/Y9BaV2qtr9Zaj9NaX6u1rnZtL9Fa/9BN+c+0\n1jd2PJIIJU/c8EdwhFHR9rsdNkMd546VrtSic4MiBpEQF05Nbce7mCaLiagISYwHsqzELIYNh7vu\nglhXi3FlpfPfnd8568zRvCQArr6y77QuXZN1DT+b/DOGRCdzoLCqzWuNFpvMzyD6tSZ7E4mJYDA6\nk468PHhtGRw9diYB+89LLve0uwigysrKNl2Q29uzZw9nn312y/PNmzczffp0li5dislkaumKvXLl\nStatW0d1dTV2u51Zs2Zx/fXXU1ZWxgsvvMBPfvITDh061HKcNWvWsHHjRvLz88nJyWHGjBk8+eST\nlJWV4XA4eP75573+HaZNm4bJZOLAgQPY7Xbefvtt7rzzzh68G22NHTuWrVu3YjKZePTRR7nzzjs5\ndeoU4BwHvHTpUrZv347JZGL9+vVkZGR4PFbr9wecrauTJ0+mpKSETZs2sWTJEtavX9/h/c3KyvJY\ntifHb7Zq1So++eQTCgoK2L17N6+//jrgvEkyc+ZMMjMzKSwspLi4mNmzZ6O19iqO8ePHezVuPRDk\nKiv8IjkmmehBNo4dO7PNZDFRVQmJMTI+SHRNhVnJL+y4lvGpMguNDdJiMJBFhkWigOhoyMiE6FYT\nTzcv82WmlLQRMPuG0cEJsgeGxw5n6sippA4ZxK6GHHac3AE4WydO11UwZpTcVBT9V2ZiJgYDHCtq\nBM7MOt9QD8052NmjEzzsLfypsrKSlStXcvvttwOwdetWLrnkEtasWdPSMthadXU1cXFxHba3bmlV\nSvHggw8yYsQIIiMj+eqrrzCbzcyfP5+wsDCuuOIKZs6cyZtvvtlSft68eQwdOpS0tDSmT5/OtGnT\nmDRpEpGRkfz4xz9m586d3fq97rrrLpYvX86GDRuYMGECI0aM6Nb+7txyyy2kpDh799x2222cddZZ\nbNu2DQCj0YjFYmHfvn1YrVbS09PbjF1urf37880331BeXs7DDz9MWFgYmZmZ3HvvvaxcubLDvt6U\n7e7xm8unpKSQmJjIrFmzWsYzb9u2jZMnT/L0008THR1NZGQkF198Mdu2bfMq5ri4uG619vtT37mV\nLvqUCGMEMTGQl9/AD37gnEHyi6IvqK+H8eMlqRFdSxmUxpFjTR22KwVjRyYGISIRSqaPns6Wwi18\n/0L4/oXw8svO7UcNHwNQdiqMC9InMjZpbBCj7Jn4ZDP7t57i8t8c5s1HZ2Jz2KizVREVLpds0X/d\nNP4m3tq4j1MNp3n525dpqIdp08ChYeJECJOOQkGzfft2rrvuOp555hkAzGYz0dHRzJw5k2+//bZD\n+cTERGprO65J3b4b/KhWswmWlJS0eQ4wevRoSkpKWp4PH35mRdfo6Og2z6Oioqirq/P6d1JKcddd\ndzF9+nQKCgo8dqM2Go1YrW2Xj7RarYSHh3coC7B8+XKeffZZjrlahurq6qhwdZ8cO3YsS5YsYeHC\nhezbt4/rrruOv/71r6Smpro9Vuv3o7CwkJKSEhITz3z/sdvtXHbZZR3287Zsd4/fnPCD8/1v/r8p\nKipi9OjRGAxt21u9jcNkMrUpE0xylRV+MzQhlv1HzIAzMXY0xkHxFHxwQ04MAEkJRk4f6TiGqclu\nk67UgrFJY9lSuKXD9pYJ2wx24hrO65PjETMznDHX1cKHB9eiHVBYCFlXR3axpxB9V0x4DOenTGaJ\ncRVbjkBxCYw9CyaOG8QTVz1BmGFgf2WdmzPXJ8d5adZL3d7n2muv5cUXX+TWW28FzrT8mkwmrr76\n6g7lzzvvPA4ePMiFF17Y6XFbfz6npaVRVFSE1rple2FhIeecc47H/b0ZD9yZ5hbbdevWsWzZMo9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BBCCCH6t5BMjDsxTyn1nVLqVaVUQrCDEUIIIYQQQgjR9/WlxPjvQCZwPnASeCa44QghhBBC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\nc8mxamwkGlC7tsCoTiNk4jmdOoqtsJTo1a47gFQMcJuETIShTx+6f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0vTa9HM1Go3zWFM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rFFZvnXM+Y+Id3jQJJJSVWil1QCn1VaXUBgDNAJ4AcGVS9iwB9lAy48bUyI4XzxzhiwYv\nMsOzM5G1mQLOnnd2UFkLjhpTtE5YBrNF3NkJzG6P7uJuZT3ews3RrCsMrXPuZFPnJly6+NKgZdEk\nmoo0h/r0vtNdX8vGEbxkdThu7doaU6i2W4I1u6rC0A6MdFvdthqdVaERBlaZKBVYnl+elrnpk1Ws\nZdGMc1A2fo8jmV09G9PLpmNn7054xIOPLvkoAODdw++arzt1Fhq8EpgmZySkq6oMNKKYdyS7eMRj\nnjvtnUNmh6fLn6yxgX9PSr+klc5WSr2llLpPKbUiWduM18oZwT3Xt6y8Baf0BFLAHlOB6dC3rroV\n141cF3GbvXW92DFnBxZOWzghR4wnU+NxVuUszKnV8bFe8WK8Z3zChKlTahmdVvbv6IaN+v+e7sCI\n8fIhYNXqKLZp25a1vu5Zc89yfd+MskAip+rCateb2IqCipBRvvc+eC/ifkVq0Nm/85EaTNEmbUoF\np5ufAl9BSIdBKqQjAVWynNx9clLDn2limsiNhbbKNlwzdA2GW4dx74Z7zU5Aa14Yr8frOp3DOvUk\nx5P8XAWUOiKCG0dvNDt1N3RsQHl+Ocb9lfqKLYnTjGs2UbolrWGcTew3hBUFFVg5c6W53Bgx3tq1\nFRUFFVGHMS1vWY5z55+bksQxU100pVXszpl3Drb3bEdRbtGESWxGqWVkwH3n8DsAAvP6Ci3TnPL9\ng8SC+MKprdMM3M4FCweBWkuZ8yuWXoELFlwQsl4qbnBL8vTvwN6gtycJc4t8ydRNt31/rPWOU6mn\ntgdXLb8KVy+/Oi2flyzH1fG0dNIyQip1JlOHdaKsHY7hMDJhYqsrrjNrIRudxWWlwLnnATv9EfTz\nB4Aaf/9fJiJgaGqblA3jSIyG8dpZa+N6f31xfdbMN5ssLlhwAe5Ye0dM71nUtCjmLLQ0uW2ZvQUA\nzBwDO+boK21ZOXC6Q/6meBoWxgiH04itMf993txA3XRjf6K98Yt3vww3jt7ouDxcgrtESlsli/Ez\nZ6LjsbW8Na7OuUwqzy835/m1VbZleG8oHqOtoxhrH8v0bmSUcc60l8WLhfXcys6Giclj+bMtGAiU\nchpoHMjMDtGUNaW63oxkL+Hmr0QrG+abxSLbQ698Hh97gilhJXkluHb4WjNDrnGTJAiMGufmAo3+\nKjfR3ERZQ/ysFk5bGHbdeEfaSvJKEhqlM8otxXKDuKBxAb77zHfj/sx4NZY04pX3XoGIoKW8JeR3\nPZnruSbKIx5zNKUivwLburehvrg+6Z+T7deOiay/vj+mmrCGydT4ayptwmfWfCau9zKaYXJbMWMF\nk61S2k2pEeO+uj7cs/4etJS3pKUcCRGlX1NpU9gGlc8HbPBPp42mk8xe+i2chuKGuG50rXb27kxK\niGy824i2Dm4y/N3w3wHQIfCzq2fjnvX3BL3eUt6Cz677bNr2ZyKxJ2hb07YGfXV9Sf8cNj4olUTE\nnP4RL+v5nh052a8sr8xxapHdZOoAooljyg3RuY3+ENHUctbcs1BdWB1xPWsmzebSZvOx2w1YQ3ED\nnsSTcTdMBRJTY6SyoBJvHXor6vUjhXQvb1ke9bYSJSL47LrPhh0V4IiBs2gyl9PkxMafZpxjT+k5\nBavbVuPQkUOMMpkARATzGkJrsNsNtwxHXIco2XhlJaIpaUnzErRXtUdcz9prvaFjQ0zru3EKw7aK\npVFdV1wX9bpz6+e61FzO3MggG77xYeNo6pqKI2m3rLrFLM9kMDqHqgqrMKtyFnrreqfk72Yymd8w\n33wcy7WNKFmm3IgxEVG8knHTNThtEDMqZuAX+37hur1YGqkbOzZix5wd+NLjX8KL774Ydt0LF14Y\n075S9uKIMU0llQWVuHPtnUHLxueM49CRQxnaI0oFe+cHUbqxYUxEFAcj87WdMZLn1ridWTEzYgM7\nlhFjn8eHuuI69NT2RGwY0+Swrn0dFjXpue8jrSPoqe3J8B5RNOqL6/HqgVcT3g4TVWoLGhdkehco\nyazh8USZMGHOriJyPYBzAez3L7pKKfX9zO3RxMLwIiLtjP4z8I9P/mNC2/jcus+ZpXLs0Xm8FQAA\nDiFJREFUovmuGRf/7ppux/fHE9Yca2itvfFtZPKm7GeUJQOAHb07MrgnlAmD0wZTkoGcKN3m1s/F\n3hf2hizvqulK/84QYWLNMVYAbldKzfP/Y6OYiCJa07Ym6Hk8pdY2dW4Keu7WKI5WcW4xAGBx02Jz\n2br2debjZGSljtWy6ctw+4m3p/1ziSg2HvGgtbw107tBlLBT55zquDwT10AiYAKNGPtx2JOIYrKx\ncyP+68X/wvtH3gcQX9IiowZ6NMxQ6jAXdqfM0Ftmb4FHPOio6sDrB18P+xlFuUUhyxKpre4RDzzi\ncdwuERFRKiQjzwZRMk2kEWMAuFhEnhSR+0WkPPLqRDTV5XpzcfuJt+Pc+eem/LM6qzvNx/Fc2Dd1\nbkJhTiFWz1wdUtPX6jNrPhOy7ITmE+Ia8f3Chi8wkRMREWUNzqOnTMmquyEReVREnnL4twnAvQBm\nAJgL4M8A/j6jO0tEE4aIYFblrJR/zsaOjVHtSzTrxFpzXURiGvE1ajgz/wBRetQU1fCGnygKdUUs\n1USZkVVnaKXU6mjWE5EvAfi22+vXX3+9+XhkZAQjIyOJ7hoRTRKJzg8Ox9rIDBdKHW+YWEdVB555\n85m43ms30jpiZjYmotQ7f+B8HD1+NNO7QZSVrJ1G7LAlJ3v37sXevXtT+hlZ1TAOR0QalFJ/9j/d\nCuApt3WtDWMiIgAoyy/D+JxxtJS14KYVN6X887J9jpSIoDCnMNO7QTRl5HhzkOPNyfRuEGWlPF9e\n1l83KbPsg5033HBD0j8jq0KpI7hNRH4jIk8CGAZwWaZ3aCKJJ+EQ0WTiEQ9WzFgBEYkpmRYQXyO3\nMKcQ/fX9IcsFguLcYsfXIuEILxERTUbnzT8v07tANHFGjJVSZ2R6H4iIIjFCwApzCrF74W7HdXwe\nn+tr4SybvgwPPPlAQvtHFIvqwmq0VbZlejeIaJK6ZPEl8IoXndWd+Nm+n2V6d2iKmzANYyKiiSTT\nYcr5vvyMfj5NDuX55fj4CR/P9G4Q0STVXdOd6V0gMrFhPEUwkQFR/CI1cqsKqrKqBvB1I9cxqycR\nERFRDCbSHGMioozoqenBp1Z/yvX1hpKGuGoIRzK/YX7EdQpyCkKWNZY0xlzuKVvkefMm7L4TERHR\nxMUR4yli2fRlMSccIiJNRFCWX5b2z3UbhVZKAQLcNXbXpMty++H5H2ZJGyKiKShcmUOidGDDeIro\nq+tDX11fpneDaNKLlAE+mdMaJlujGOB8MyIiIsoMhlITERERERHRlMaGMRHRBMNkekRENNlwyh9l\nGkOpiYiyXGVBpfl4z8Y9GdwTIiKi1BhrH8PqttWZ3g2awtgwJiLKcsumL4sqQzUREdFEJSLI9eZm\nejdoCmMoNRFRGkVKzuXEIx4U5xanYG+IiIiICGDDmIiIiIiIiKY4NoyJiLIUazoSERERpQcbxkRE\nacSM0kRERETZhw1jIiIiIiIimtLYMCYiIiIiIqIpjQ1jIqIkYqg0ERER0cTDhjERERERERFNaWwY\nExGlUVNpU6Z3gYiIiIhsfJneASKiqWLPxj2Z3gUiIiIicsCGMRFREnVVd+HVplczvRtEREREFAM2\njImIkmhGxQzMqJiRlG21lLfgsZceS8q2iIiIiMidKKUyvQ9JJSJqsv1MREREREREpIkIlFJJLQWS\ndcm3RGS7iPxORI6JyHzba1eJyLMi8rSIrMnUPhIREREREdHkkXUNYwBPAdgK4D+sC0WkG8A4gG4A\nawHcIyLZuP80yezduzfTu0CTCI8nSjYeU5RsPKYo2XhM0USQdQ1LpdTTSqlnHF7aDOBBpdQRpdQL\nAJ4DMJjWnaMpiSdzSiYeT5RsPKYo2XhMUbLxmKKJIOsaxmE0AnjZ8vxlANMytC9EREREREQ0SWQk\nK7WIPAqg3uGlq5VS345hU8yyRURERERERAnJ2qzUIvJjAJcrpR73P78SAJRSt/qffx/AdUqpn9ne\nl50/EBERERERESVFsrNSZ3sdY+sP+y0AXxOR26FDqNsB/Nz+hmT/goiIiIiIiGhyy7o5xiKyVURe\nArAYwHdF5HsAoJT6PYBvAvg9gO8B2M2CxURERERERJSorA2lJiIiIiIiIkqHrBsxjpeIrBWRp0Xk\nWRH520zvD2UvEWkWkR+LyO9E5Lci8hH/8koReVREnhGRH4pIueU9V/mPradFZI1l+YCIPOV/7bOZ\n+HkoO4iIV0SeEJFv+5/zeKK4iUi5iPyziPxBRH4vIot4TFEiROQy/zXvKRH5mojk8ZiiWIjIl0Xk\nNRF5yrIsaceQ/5j8hn/5f4tIS/p+OsoEl2Pq0/5r35Mi8q8iUmZ5LaXH1KRoGIuIF8BdANYC6Aaw\nQ0S6MrtXlMWOALhMKdUDHbL/N/7j5UoAjyqlOgD8yP8cItINYBz62FoL4B4RMeay3wvgw0qpdgDt\nIrI2vT8KZZFLoKd6GGE4PJ4oEZ8F8IhSqgtAH4CnwWOK4iQi0wBcDGBAKdULwAvgVPCYoth8Bfp4\nsErmMfRhAG/6l98B4LZU/jCUFZyOqR8C6FFK9QN4BsBVQHqOqUnRMAYwCOA5pdQLSqkjAL4OYHOG\n94mylFLqVaXUr/2PDwD4A3RCt00A/sG/2j8A2OJ/vBnAg0qpI0qpFwA8B2CRiDQAKFFKGUng/tHy\nHppCRKQJwBiALyGQNJDHE8XF3zu+XCn1ZQBQSh1VSr0LHlOUGB+AQhHxASgE8Ap4TFEMlFL/CeBt\n2+JkHkPWbf0LgJVJ/yEoqzgdU0qpR5VSx/1Pfwagyf845cfUZGkYTwPwkuX5y/5lRGGJSCuAedBf\nvDql1Gv+l14DUOd/3Ah9TBmM48u+fB943E1VdwD4GIDjlmU8niheMwDsF5GviMjjIvJFESkCjymK\nk1JqH4C/B/AidIP4HaXUo+AxRYlL5jFk3s8rpY4CeFdEKlO03zQxnAPgEf/jlB9Tk6VhzAxiFDMR\nKYbuPbpEKfWe9TV/xnMeVxSRiGwA8LpS6gkEl5gz8XiiGPkAzAdwj1JqPoCD8IcnGnhMUSxEpAJ6\n5KQV+iayWEROt67DY4oSxWOIkklErgHwgVLqa+n6zMnSMN4HoNnyvBnBPQdEQUQkB7pR/IBS6iH/\n4tdEpN7/egOA1/3L7cdXE/TxtQ+B8A5j+b5U7jdlpaUANonInwA8CGCFiDwAHk8Uv5cBvKyU+oX/\n+T9DN5Rf5TFFcVoF4E9KqTf9oyb/CmAJeExR4pJxrXvZ8p7p/m35AJQppd5K3a5TthKRs6CnqJ1m\nWZzyY2qyNIx/CT3RulVEcqEnZn8rw/tEWco/Uf9+AL9XSt1peelbAM70Pz4TwEOW5aeKSK6IzADQ\nDuDnSqlXAfxFdLZYAfAhy3toilBKXa2UalZKzYBOZvNvSqkPgccTxcl/LLwkIh3+RasA/A7At8Fj\niuLzvwAWi0iB/1hYBZ0skMcUJSoZ17qHHbZ1MnQyL5pi/ImzPgZgs1LqsOWllB9TviT+HBmjlDoq\nIhcB+AF0psX7lVJ/yPBuUfY6AcDpAH4jIk/4l10F4FYA3xSRDwN4AcApAKCU+r2IfBP6JuIogN0q\nUAB8N4D/C6AAOoPs99P1Q1DWMo4NHk+UiIsBfNXf2fs/AM6Gvr7xmKKYKaV+LiL/DOBx6GPkcQD3\nASgBjymKkog8CGAYQLWIvATg75Dca939AB4QkWcBvAnd2UyTmMMxdR30PXkugEf9Sad/qpTanY5j\nSgLbIyIiIiIiIpp6JksoNREREREREVFc2DAmIiIiIiKiKY0NYyIiIiIiIprS2DAmIiIiIiKiKY0N\nYyIiIiIiIprS2DAmIiIiIiKiKY0NYyIiohQSkWMi8oT/3+Mi0iIij/lfaxWRp/yP+0VkXRI+7xoR\n+a2IPOn/zIX+5ZeKSEGi2yciIpqMfJneASIioknufaXUPNuyExzWmwdgAMD3ot2wiPiUUkctz5cA\nWA9gnlLqiIhUAsjzv3wJgAcAHIpl54mIiKYCjhgTERGlmYgcsD3PAXAjgHH/KO92ESkSkS+LyM/8\nI82b/OueJSLfEpEfAXjUtul6AG8opY4AgFLqLaXUn0XkIwAaAfzY/z6IyBoR+YmI/EpEvikiRf7l\nL4jIbSLyG/9nt6X0l0FERJQF2DAmIiJKrQJLKPW/+Jcp6wr+huy1AL6ulJqnlPonANcA+JFSahGA\nFQA+LSKF/rfMA7BNKTVq+6wfAmgWkT+KyN0iMuTf/ucAvAJgRCm1UkSq/dtfqZQaAPArAB+17Ns7\nSqk+AHcBuDNpvwkiIqIsxVBqIiKi1DrkEErtRPz/DGsAbBSRK/zP8wBMh264PqqUese+AaXUQREZ\nALAcwCiAb4jIlUqpf7CtuhhAN4CfiAgA5AL4ieX1B/3/fx3AHVHsOxER0YTGhjEREVH2Okkp9ax1\ngYgsAnDQ7Q1KqeMA/h3Av/sTe50JwN4wBnTjemcU+6Air0JERDSxMZSaiIgoO/wFQInl+Q8AfMR4\nIiLGqLN1VDmIiHSISLtl0TwAL/gfvweg1P/4ZwBOMOYP++czW983bvnfOpJMREQ0KXHEmIiIKLWc\nRlyVw+MfA7hSRJ4AcDOAmwDcKSK/ge7Ifh7AJv/6bqO4xQA+LyLlAI4CeBbALv9r9wH4vojs888z\nPgvAgyJiZK2+xr8+AFSIyJMADgPYEcsPS0RENBGJUoyQIiIiIk1E/gRgQCn1Vqb3hYiIKF0YSk1E\nRERW7DEnIqIphyPGRERERERENKVxxJiIiIiIiIimNDaMiYiIiIiIaEpjw5iIiIiIiIimNDaMiYiI\niIiIaEpjw5iIiIiIiIimNDaMiYiIiIiIaEr7/3g3AfegNhbKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac168d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "plt.subplot(511)\n",
    "plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n",
    "plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n",
    "\n",
    "plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n",
    "plt.legend(loc='best')\n",
    "plt.ylabel('Position (relative to start) [m]')\n",
    "\n",
    "plt.subplot(512)\n",
    "plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n",
    "plt.ylabel('Course')\n",
    "plt.legend(loc='best')\n",
    "           \n",
    "plt.subplot(513)\n",
    "plt.step(range(len(measurements[0])),x3, label='$v$')\n",
    "plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)', alpha=0.6)\n",
    "plt.ylabel('Velocity')\n",
    "plt.ylim([0, 30])\n",
    "plt.legend(loc='best')\n",
    "\n",
    "plt.subplot(514)\n",
    "plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n",
    "plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)', alpha=0.6)\n",
    "plt.ylabel('Yaw Rate')\n",
    "plt.ylim([-0.6, 0.6])\n",
    "plt.legend(loc='best')\n",
    "\n",
    "plt.subplot(515)\n",
    "plt.step(range(len(measurements[0])),x5, label='$a$')\n",
    "plt.step(range(len(measurements[0])),ax, label='$a$ (from IMU as reference)', alpha=0.6)\n",
    "plt.ylabel('Acceleration')\n",
    "#plt.ylim([-0.6, 0.6])\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('Filter Step')\n",
    "\n",
    "plt.savefig('Extended-Kalman-Filter-CTRA-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%pylab --no-import-all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUAAAAAWCAYAAACxMEX0AAAABHNCSVQICAgIfAhkiAAABT5JREFU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\n",
      "text/latex": [
       "$$\\left ( -100.0, \\quad 700.0, \\quad -50.0, \\quad 400.0\\right )$$"
      ],
      "text/plain": [
       "(-100.0, 700.0, -50.0, 400.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h4Xz55ZdF3Q0pBAp0RURE8iE6GlavPgjMdlMaDvwA/AisAH4HdgMTgYa5nHkr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65MxS6ktEvN+pEkSZK0fJzRVZ82blw7d975/TIVAZzpTK4kSZKUIQZd9VmtrXDWWScBb5Wp+hr5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\nmsr/B78ScCVg+vWHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083a1d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "# EKF State\n",
    "plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='k', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "# Start/Goal\n",
    "plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n",
    "plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.ylabel('Y [m]')\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "plt.axis('equal')\n",
    "#plt.tight_layout()\n",
    "\n",
    "#plt.savefig('Extended-Kalman-Filter-CTRA-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Detailed View"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10dad3790>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uLiJEcrH87s1YeZBuO6oQ6fLIpt5D+/D6hf/o905JCQQyufSwukjUdJE/tNbP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\nFkIIIYQQIpX9P3UdOgudoNblAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108bf7090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,9))\n",
    "\n",
    "plt.subplot(221)\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(70, 130)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(140, 200)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "\n",
    "\n",
    "plt.subplot(222)\n",
    "\n",
    "# EKF State\n",
    "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "# Measurements\n",
    "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "#cbar=plt.colorbar(ticks=np.arange(20))\n",
    "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "#cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "plt.xlabel('X [m]')\n",
    "plt.xlim(160, 260)\n",
    "plt.ylabel('Y [m]')\n",
    "plt.ylim(110, 160)\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Write Google Earth KML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert back from Meters to Lat/Lon (WGS84)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "latekf = latitude[0] + np.divide(x1,arc)\n",
    "lonekf = longitude[0]+ np.divide(x0,np.multiply(arc,np.cos(latitude*np.pi/180.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data for KML Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coordinates and timestamps to be used to locate the car model in time and space\n",
    "The value can be expressed as yyyy-mm-ddThh:mm:sszzzzzz, where T is the separator between the date and the time, and the time zone is either Z (for UTC) or zzzzzz, which represents ±hh:mm in relation to UTC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "car={}\n",
    "car['when']=[]\n",
    "car['coord']=[]\n",
    "car['gps']=[]\n",
    "for i in range(len(millis)):\n",
    "    d=datetime.datetime.fromtimestamp(millis[i]/1000.0)\n",
    "    car[\"when\"].append(d.strftime(\"%Y-%m-%dT%H:%M:%SZ\"))\n",
    "    car[\"coord\"].append((lonekf[i], latekf[i], 0))\n",
    "    car[\"gps\"].append((longitude[i], latitude[i], 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from simplekml import Kml, Model, AltitudeMode, Orientation, Scale, Style, Color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The model path and scale variables\n",
    "car_dae = r'https://raw.githubusercontent.com/balzer82/Kalman/master/car-model.dae'\n",
    "car_scale = 1.0\n",
    "\n",
    "# Create the KML document\n",
    "kml = Kml(name=d.strftime(\"%Y-%m-%d %H:%M\"), open=1)\n",
    "\n",
    "# Create the model\n",
    "model_car = Model(altitudemode=AltitudeMode.clamptoground,\n",
    "                            orientation=Orientation(heading=75.0),\n",
    "                            scale=Scale(x=car_scale, y=car_scale, z=car_scale))\n",
    "\n",
    "# Create the track\n",
    "trk = kml.newgxtrack(name=\"EKF\", altitudemode=AltitudeMode.clamptoground,\n",
    "                     description=\"State Estimation from Extended Kalman Filter with CTRA Model\")\n",
    "\n",
    "# Attach the model to the track\n",
    "trk.model = model_car\n",
    "trk.model.link.href = car_dae\n",
    "\n",
    "# Add all the information to the track\n",
    "trk.newwhen(car[\"when\"])\n",
    "trk.newgxcoord(car[\"coord\"])\n",
    "\n",
    "# Style of the Track\n",
    "trk.iconstyle.icon.href = \"\"\n",
    "trk.labelstyle.scale = 1\n",
    "trk.linestyle.width = 4\n",
    "trk.linestyle.color = '7fff0000'\n",
    "\n",
    "# Add GPS measurement marker\n",
    "fol = kml.newfolder(name=\"GPS Measurements\")\n",
    "sharedstyle = Style()\n",
    "sharedstyle.iconstyle.icon.href = 'http://maps.google.com/mapfiles/kml/shapes/placemark_circle.png'\n",
    "\n",
    "for m in range(len(latitude)):\n",
    "    if GPS[m]:\n",
    "        pnt = fol.newpoint(coords = [(longitude[m],latitude[m])])\n",
    "        pnt.style = sharedstyle\n",
    "\n",
    "# Saving\n",
    "kml.savekmz(\"Extended-Kalman-Filter-CTRA.kmz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exported KMZ File for Google Earth\n"
     ]
    }
   ],
   "source": [
    "print('Exported KMZ File for Google Earth')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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